Allen Downey Problem-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction: Finding Prevalence from Observations\n",
    "\n",
    "In this notebook, we'll look at solving the following statistics problem in a Bayesian Framework. (Problem courtesy of Allen Downey on Twitter: [tweet link](https://twitter.com/AllenDowney/status/1063460263716892674))\n",
    "\n",
    "> Today's Bayesian problem of the week: Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don't know how many of each there are.\n",
    "During the tour, we see 3 lions, 2 tigers, and 1 bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species.\n",
    "What is the probability that the next animal we see is a bear?\n",
    "\n",
    "> Solution next week!\n",
    "\n",
    "Our goal is to estimate the percentage of each species and determine the probability that the next animal is a bear. \n",
    "\n",
    "## Bayesian Approach\n",
    "\n",
    "In a frequentist view, we would just use the observed animals to estimate the prevalence and let the data completely speak for itself. In contrast, in a Bayesian framework, we incorporate priors, which here are set to be equal for all species. In the case of infinite observations, the effect of the priors disappear and we only use the data. Due to the limited number of observations, the _priors_ will still have an large effect on the prevalence we obtain, and the _uncertainty_ will be large. \n",
    "\n",
    "### PyMC3 and MCMC\n",
    "\n",
    "To solve the problem, we'll build a model in [PyMC3](https://docs.pymc.io/) and then use a variant of Markov Chain Monte Carlo (the No-UTurn Sampler specifically) to draw samples from the posterior. With enough samples, the estimate will converge on the true posterior. Along with maximum likelihood estimates (such as the mean of sampled) values, MCMC also gives us built in uncertainty.\n",
    "\n",
    "## Model\n",
    "\n",
    "The overall system is as follows (each part will be explained):\n",
    "\n",
    "1. The underlying model is a multinomial distribution with parameters $p_k$\n",
    "2. The _prior_ distribution of $p_k$ is a Dirichlet Distribution\n",
    "3. The $\\alpha$ vector is a parameter of the prior Dirichlet Distribution, hence a _hyperparameter_\n",
    "4. The prior on $\\alpha$ is uniform and is referred to as a _hyperprior_\n",
    "\n",
    "## Multinomial Distribution\n",
    "\n",
    "This problem is a classic example of the [multinomial distribution](https://en.wikipedia.org/wiki/Multinomial_distribution) which describes a situation in which we have n independent trials, each with k possible outcomes. With the wildlife preserve problem, n = 6 and k = 3. It is characterized by the probability of each outcome, $p_k$ which must sum to 1. Our goal is to find $p_\\text{lions}$, $p_\\text{tigers}$, $p_\\text{bears}$ given the observations lions: 3, tigers: 2, and bears: 1.\n",
    "\n",
    "## Dirichlet Distribution\n",
    "\n",
    "The prior for a multinomial distribution in Bayesian statistics is a [Dirichlet distribution](https://en.wikipedia.org/wiki/Dirichlet_distribution). (Together, a multinomial distribution with a dirichlet prior is called, not surprisingly, a [Dirichlet-Multinomial Distribution](https://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution). The Dirichlet distribution is characterized by $\\alpha$, the concentration hyperparameter vector. \n",
    "\n",
    "### Hyperparameters and Hyperpriors\n",
    "\n",
    "The $\\alpha$ vector is a [hyperparameter](https://en.wikipedia.org/wiki/Hyperparameter), a parameter of a prior distribution. This vector in turn has its _own prior_ distribution which is called a [_hyperprior_](https://en.wikipedia.org/wiki/Hyperprior). \n",
    "The hyperprior can be thought of as pseudo-counts, which record the number of observations already seen before gathering the data. We want a uniform hyperprior reflecting the chance of observing any species is the same, so we set $\\alpha = [1, 1, 1]$. \n",
    "\n",
    "### Expected Value\n",
    "\n",
    "One way to get a single point estimate of the prevalence is to use the expected value of the posterior for $p_k$. From Wikipedia, our model is:\n",
    "\n",
    "$${\\begin{array}{lclcl}\\mathbf {c} &=&(c_{1},\\ldots ,c_{K})&=&{\\text{number of occurrences of category }}i=\\sum _{j=1}^{N}[x_{j}=i]\\\\\\mathbf {p} \\mid \\mathbb {X} ,{\\boldsymbol {\\alpha }}&\\sim &\\operatorname {Dir} (K,\\mathbf {c} +{\\boldsymbol {\\alpha }})&=&\\operatorname {Dir} (K,c_{1}+\\alpha _{1},\\ldots ,c_{K}+\\alpha _{K})\\end{array}}$$\n",
    "\n",
    "which, after filling in the data (number of occurrences) and the hyperpriors becomes:\n",
    "\n",
    "$${\\displaystyle \\operatorname {Dir} (K,c_{lions}+\\alpha_{lions}, c_{tigers}+\\alpha_{tigers}, c_{bears}+\\alpha_{bears})}$$\n",
    "$${\\displaystyle \\operatorname {Dir} (9, 4, 3, 2)}$$\n",
    "\n",
    "For a single observation (n = 1), this becomes a [categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) and we can get point estimate using the expected value:\n",
    "\n",
    "$${\\displaystyle \\operatorname {E} [p_{i}\\mid \\mathbb {X} ,{\\boldsymbol {\\alpha }}]={\\frac {c_{i}+\\alpha _{i}}{N+\\sum _{k}\\alpha _{k}}}}$$\n",
    "\n",
    "Therefore, from the viewpoint of a single observation, we get the expected prevalances:\n",
    "\n",
    "$$p_{lions} = \\frac{4}{9} = 44.4\\%$$\n",
    "$$p_{tigers} = \\frac{3}{9} = 33.3\\%$$\n",
    "$$p_{bears} = \\frac{2}{9} = 22.2\\%$$\n",
    "\n",
    "However, at least to me, this result is unsatisfying because it does not show our uncertainty due to the limited amount of data. For that, we turn to Bayesian modeling and sampling from the posterior with MCMC. For that, we'll move over to PyMC3!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Visualizations\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "plt.style.use('fivethirtyeight')\n",
    "plt.rcParams['font.size'] = 22\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore', category=FutureWarning)\n",
    "\n",
    "import pymc3 as pm\n",
    "\n",
    "# Helper functions\n",
    "from utils import draw_pdf_contours, Dirichlet, plot_points, annotate_plot, add_legend, display_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Specifics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# observations\n",
    "animals = ['lions', 'tigers', 'bears']\n",
    "c = np.array([3, 2, 1])\n",
    "\n",
    "# hyperparameters (initially all equal)\n",
    "alphas = np.array([1, 1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expected Value\n",
    "\n",
    "https://en.wikipedia.org/wiki/Categorical_distribution#Bayesian_inference_using_conjugate_prior\n",
    "\n",
    "$${\\displaystyle \\operatorname {E} [p_{i}\\mid \\mathbb {X} ,{\\boldsymbol {\\alpha }}]={\\frac {c_{i}+\\alpha _{i}}{N+\\sum _{k}\\alpha _{k}}}}$$\n",
    "\n",
    "The expected value is simply as calculated above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 44.44%.\n",
      "Species: tigers   Prevalence: 33.33%.\n",
      "Species: bears    Prevalence: 22.22%.\n"
     ]
    }
   ],
   "source": [
    "display_probs(dict(zip(animals, (alphas + c) / (c.sum() + alphas.sum()))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 44.44%.\n",
      "Species: tigers   Prevalence: 33.33%.\n",
      "Species: bears    Prevalence: 22.22%.\n"
     ]
    }
   ],
   "source": [
    "display_probs(dict(zip(animals, (4/9, 3/9, 2/9))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum A Posterior Estimation\n",
    "\n",
    "The maximum a posterior (MAP) estimate is simply going to be the prevalence seen in the data. This is a frequentist way of viewing the world.\n",
    "\n",
    "https://en.wikipedia.org/wiki/Categorical_distribution#MAP_estimation\n",
    "\n",
    "$${\\displaystyle \\operatorname {arg\\,max} \\limits _{\\mathbf {p} }p(\\mathbf {p} \\mid \\mathbb {X} )={\\frac {\\alpha _{i}+c_{i}-1}{\\sum _{i}(\\alpha _{i}+c_{i}-1)}},\\qquad \\forall i\\;\\alpha _{i}+c_{i}>1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 50.00%.\n",
      "Species: tigers   Prevalence: 33.33%.\n",
      "Species: bears    Prevalence: 16.67%.\n"
     ]
    }
   ],
   "source": [
    "display_probs(dict(zip(animals, (alphas + c - 1) / sum(alphas + c - 1))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 50.00%.\n",
      "Species: tigers   Prevalence: 33.33%.\n",
      "Species: bears    Prevalence: 16.67%.\n"
     ]
    }
   ],
   "source": [
    "display_probs(dict(zip(animals, c / c.sum())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Model\n",
    "\n",
    "Now we'll get into building and sampling from a Bayesian model. As a reminder, we are using a multinomial as our model, a Dirichlet distribution as the prior, and uniform _hyperpriors_. The objective is to find the _parameters_ of the prior, $p_k$ which are the probability of each species given the evidence. \n",
    "\n",
    "$$(\\mathbf {p} \\mid \\mathbb  {X}, {\\boldsymbol {\\alpha}})$$\n",
    "\n",
    "https://en.wikipedia.org/wiki/Categorical_distribution#Bayesian_inference_using_conjugate_prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING (theano.gof.compilelock): Overriding existing lock by dead process '9036' (I am process '13812')\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    # Dirichlet hyperparameters are uniform hyperpriors\n",
    "    hyperpriors = pm.Uniform('hyperpriors', shape = 3, observed = alphas)\n",
    "    # Probabilities for each species\n",
    "    parameters = pm.Dirichlet('parameters', a=hyperpriors, shape=3)\n",
    "    # Observed data is a multinomial distribution with 6 trials\n",
    "    observed_data = pm.Multinomial(\n",
    "        'observed_data', n=6, p=parameters, shape=3, observed=c)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "            \\begin{array}{rcl}\n",
       "            parameters &\\sim & \\text{Dirichlet}(\\mathit{a}=\\text{hyperpriors})\\\\\\text{hyperpriors} &\\sim & \\text{Uniform}(\\mathit{lower}=0.0,~\\mathit{upper}=1.0)\\\\observed_data &\\sim & \\text{Multinomial}(\\mathit{n}=6, \\mathit{p}=f(\\text{parameters},~f(f(\\text{parameters}))))\n",
       "            \\end{array}\n",
       "            $$"
      ],
      "text/plain": [
       "<pymc3.model.Model at 0x1ebb54cae48>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling from the Model\n",
    "\n",
    "The cell below samples 1000 draws from the posterior in 2 chains. We use 500 samples for tuning (1000 total because of the 2 chains). This means that for each random variable - the `parameters` - we will have 3000 total samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:07<00:00, 400.42draws/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    # Sample from the posterior\n",
    "    trace = pm.sample(draws=1000, chains=2, tune=500, discard_tuned_samples=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inspecting Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.444018</td>\n",
       "      <td>0.152194</td>\n",
       "      <td>0.002562</td>\n",
       "      <td>0.152288</td>\n",
       "      <td>0.735601</td>\n",
       "      <td>2779.622971</td>\n",
       "      <td>1.000291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.330000</td>\n",
       "      <td>0.144525</td>\n",
       "      <td>0.002627</td>\n",
       "      <td>0.071472</td>\n",
       "      <td>0.610482</td>\n",
       "      <td>2727.795655</td>\n",
       "      <td>1.000087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.225982</td>\n",
       "      <td>0.130168</td>\n",
       "      <td>0.002613</td>\n",
       "      <td>0.014302</td>\n",
       "      <td>0.475272</td>\n",
       "      <td>2475.737395</td>\n",
       "      <td>0.999708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.444018  0.152194  0.002562  0.152288  0.735601  2779.622971   \n",
       "tigers  0.330000  0.144525  0.002627  0.071472  0.610482  2727.795655   \n",
       "bears   0.225982  0.130168  0.002613  0.014302  0.475272  2475.737395   \n",
       "\n",
       "            Rhat  \n",
       "lions   1.000291  \n",
       "tigers  1.000087  \n",
       "bears   0.999708  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = pm.summary(trace)\n",
    "summary.index = animals\n",
    "summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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       "      <th>tigers</th>\n",
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       "      <th>tune</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.588556</td>\n",
       "      <td>0.351780</td>\n",
       "      <td>0.059664</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.530131</td>\n",
       "      <td>0.346303</td>\n",
       "      <td>0.123566</td>\n",
       "      <td>False</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.383550</td>\n",
       "      <td>0.404125</td>\n",
       "      <td>0.212325</td>\n",
       "      <td>False</td>\n",
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       "      <th>3</th>\n",
       "      <td>0.481450</td>\n",
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       "      <td>0.305612</td>\n",
       "      <td>False</td>\n",
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       "      <th>4</th>\n",
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       "      <td>0.540885</td>\n",
       "      <td>0.139354</td>\n",
       "      <td>False</td>\n",
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      "text/plain": [
       "      lions    tigers     bears   tune\n",
       "0  0.588556  0.351780  0.059664  False\n",
       "1  0.530131  0.346303  0.123566  False\n",
       "2  0.383550  0.404125  0.212325  False\n",
       "3  0.481450  0.212938  0.305612  False\n",
       "4  0.319760  0.540885  0.139354  False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Tuning samples\n",
    "tune_df = pd.DataFrame(trace['parameters'][:1000], columns = animals)\n",
    "tune_df['tune'] = True\n",
    "\n",
    "# Samples after tuning\n",
    "trace_df = pd.DataFrame(trace['parameters'][1000:], columns = animals)\n",
    "trace_df['tune'] = False\n",
    "\n",
    "all_df = pd.concat([tune_df, trace_df])\n",
    "trace_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a single point estimate, we can use the mean of the samples after burn in. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 44.60%.\n",
      "Species: tigers   Prevalence: 32.90%.\n",
      "Species: bears    Prevalence: 22.50%.\n"
     ]
    }
   ],
   "source": [
    "# For probabilities use samples after burn in\n",
    "pvals = trace_df.iloc[:, :3].mean(axis = 0)\n",
    "display_probs(dict(zip(animals, pvals)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These numbers align nearly exactly with the expected values! However, we also get a range of uncertainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>5th percentile</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.204699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.115185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.048281</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "        5th percentile\n",
       "lions         0.204699\n",
       "tigers        0.115185\n",
       "bears         0.048281"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace_df.iloc[:, :3].apply(lambda x: np.percentile(x, 5)).to_frame().rename(columns = {0: '5th percentile'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>95th percentile</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.700873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.585362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.464277</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        95th percentile\n",
       "lions          0.700873\n",
       "tigers         0.585362\n",
       "bears          0.464277"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace_df.iloc[:, :3].apply(lambda x: np.percentile(x, 95)).to_frame().rename(columns = {0: '95th percentile'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the large amount of uncertainty in the estimates due to the limited amount of data. To see this visually, we can use some of PyMC3's built in plots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diagnostic Plots\n",
    "\n",
    "PyMC3 offers a number of [plotting options](https://docs.pymc.io/api/plots.html) for inspecting our samples.\n",
    "\n",
    "## Posterior Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ar/r2mTnw6M9mnY03a+DMGlZVreclTP3xcjZ91bZ54uEpufd3l2fOzBkZMmJkHyQHAAAAQBM0lGEphq+9bpLkyUemLrbuuVkz5//78QcmZdQOuyy0/r4br859N1690LLRu+yR953ytay90abzl2267Y7ZeJsdcv8fbs3Fpx2XF+bMzu2XXZRNt90xm4x9bea+9FIuOuWojNp+5+x2yEcaOa/ffOv0HtfNmfH0MsWaNvnePHDbDUkyf3qOuoYMH5G1XrFxnp72aB6Z8IeM2XXPZdqflcfEiRNy5EmnNhave8SQjD/u6MbiAQAAAEunoQxLsc1e++cPv/xxrj33m3nNW96VYWutk6Q1n/HDE++ev93sGX+Z/+/VhwzNmz52TMbu87asu+kWSZI///Hu/OasM3L/Ldfm2598dz59wVVZY+jwJEnXaqvlw189L2f9/QG589c/S0rJdvu9I28/5t/S1dWVa773tUy7b0I+fcFVmTPj6fzsCyfknt9elrkvvpitdtsnB/XiBn1XnH1Gr2ty7XlnLXZTvhfmzM62+x6YLXd6wzLHW3P9jfL0tEfz7FNP9DonOl/X4GEZO+7YxuLdc07vX8MAAABA72gow1Ls8JZ35fZLL8wfr7siX37vHnn13m/N6kOGZvJN1+SpaX9K96jRmT71/pSu1ebvM2Ld9fPmw45fKM6WO++ej3zjwpz1kbfnobtuzc0/OTd7/N0n5q9fc/0Ns/Uuu+eg8V9baL8npk7Ob846PW8+7PisN2pMfnD0h3L/LdfloOO/kMHDR+ZnXzg+5/7zuHzqe79MWYbpJk677fEe133hwJ0Wmrt5Udeff3aSpJSSNYYNz4avHJvXHvDevP6942off0FVqvnxAAAAAOhcGsqwFF1dXfnQl8/N9eefndsv+VFuv/TCrDZoUEbtsGvW32SzPP3UU5me+zNi3fWWGmu1QYOy67sOzUN33ZoHbrthoYbyklRVlf855R+z4SvHZo9DP5knpk7OPVdfljd/6vjs9Pa/SZI89+zMXHjS4bn/5msz5nV7NXLOS3PcL27NOhuPaizejMf/nCQZvs7SawgAAABA/9FQhhpWGzQoe33wU9nrg59aaPlP/vWTufd/f5fVhwzNK0ZvUyvWvKbp87NnLXXbG3747Tx012058vwr09XVlccemJQk2XibHeZvs8nY1yRJpt1/7wprKDdpzswZeXrao+kaNCibvPo1/Z0OAAAAAC+jq78TgJXZ4w89mBefm5Pt3/zOrLb66rX2mXrnLUkyf27lnjz16NT86mufz34fOyavGP2q1sKqNTXES88/P3+7F5+bs+yJd5CH/9iah/rVe70lg4eP6OdsAAAAAHg5GspQw5yZMxZb9tDdt2fqhDuyxrDh2e9j/7zQuql33poXX3h+sX0m3/S7XHfeWUmSHQ9478se88f/dnTWGzU6e4/79PxlG7QbyxOu+dX8ZROuuTxJao+Q7hRzZs7Iz04/IU88/GCGjFwrb/n0v/Z3SgAAAAAshSkvoIb/+tR7s/rgIXnFmG0yePiIPDZ5YiZe95skyaGn/2Cx0ca//PfP5rHJE7PlLrtnrQ02TpL8edI9mXzz75Ikb/7U8dn8Na/r8Xg3/fgHuf/W63L4Dy7PaoP++mu63qjR2XbfA3Prz87P87OfzeDhI3Pbzy/IptvtlNG77tnwWTfn2vPOytCRa6Wqqjz37Iw8/uB9mXLbDXl+9qwMGT4yH/nGhVl/8zH9nSYAAAAAS6GhDDVsv9878odf/SS/v/SivPDcnKy5/obZ5eAP5Pmnp2fr3d+02PY7Hvi+3H3lpXn47t/nj9ddkZdefDEjutfP9m8+KG/4m3/Ilju9ocdjPf3Yn3LZV8bnjeM+nY1ftf1i698z/qtZY/jwTLj6l3npxRezzV77553HfyGllEbPuUnXn392kqRr0KAMHjYia26wUcbue2DG7vPW3HfNZdls2x37OUMAAAAA6tBQhhr2/vAR2fvDRyy2/OLxiy9Lkl0P/kB2PfgDvTrWWhtslJOvmdzj+qEj18ohn/16r2InyWm3Pb7Ubf7vJbf1uPzi8UdknY1H1TpWT3EWdP+1l9eKBQAAAED/65iG8vTp0/Pkk082Fm/SpEnLtP2s2bMbO3aSzJ07t6Pj9UXMTo/XFzE7PV5fxOz0eH0Rc1XMcWU451mzZy/ze/2ilnf/VZna9Y669V5f1W6XXXbpk7gAADBQdUxDubu7O93d3Y3EmjRpUrbaaqtl2mfY0KGNHHuerq5m73fYdLy+iNnp8foiZqfH64uYnR6vL2KuijmuDOc8bOjQZX6vX1BvrhW0qF3vqFvvqR0AAHSO5jsGAAAAAAAMSBrKAAAAAADUoqEMAAAAAEAtGsoAAAAAANSioQwAAAAAQC0aygAAAAAA1DKovxMAgN6YOHFCjjzp1F7vP2v27AwbOnT+z90jhmT8cUc3kRoAAAAMWBrKAKyUugYPy9hxxzYW755zzmgsFgAAAAxUprwAAAAAAKAWDWUAAAAAAGrRUAYAAAAAoBYNZQAAAAAAatFQBgAAAACgFg1lAAAAAABqGdTfCQBAJ5g4cUKOPOnURmN2jxiS8ccd3WhMAAAA6E8aygCQpGvwsIwdd2yjMe8554xG4wEAAEB/M+UFAAAAAAC1aCgDAAAAAFCLhjIAAAAAALVoKAMAAAAAUIuGMgAAAAAAtWgoAwAAAABQy6Bl2biUsmmSzyZ5a5LuJH9K8tMkp1RV9dQyxFk3yUlJDk6yUZLphx56aE488cRssskmi21/8cUX59prr81dd92Vu+66KzNmzMghhxySs88+u3buRxxxRM4999wkyW233ZbRo0fX3heAzvPc7Fm5aPyn88frr8ysp5/KyPVekbH7vC3/5xPHZuiaa/cq5gO3Xp///MS7Us2dm33/4Z+y/+EnLrT+wpOPyG0//+HLxhiz61756Fk/nv/zeeedl8MPP7zH7c8888x85CMf6VW+AAAAsKLVbiiXUsYkuT7JBkkuTnJvktclOSrJW0spe1RVNb1GnO52nK2TXJnkgiTbnHfeeQddfvnl+fWvf50ttthioX3OOOOM3HXXXRkxYkQ23njjzJgxo27aSZLLLrss5557bkaMGJGZM2cu074AdJ7pDz2Qu357eV54/rmM3edtWX+LV+ahu27P9eefnUk3XJlPfOeSDF973WWK+dKLL+TCk4/M6kOG5vlZzy5xm7H7HJB1Nhq1xHW3X3phnnx4SrbeY78lrj/ggAOy/fbbL7Z8xx13XKY8AQAAoD8tywjlb6TVTP50VVX/MW9hKeXMJP+U5PNJPlkjzqlpNZO/XFXV0fMWfuELX6iOP/74HHPMMfmf//mfhXc49dRssskmGT16dK699tq84x3vqJ30E088kaOOOirvfve7M23atFx33XW19wWgM1182nF54fnn8o7jTs3uf/ux+ct/8aV/zXXnfSuXf/3UvOtfvrhMMafceXvmzHwm+/z9Ubn866cucZtt9z0g2+57wGLLZ894Otd8/2tZbfU1svM7/naJ+x544IE59NBDlyknAAAA6DS15lAupYxOsn+SKUm+vsjqk5M8m+SDpZThS4kzPMkH29ufvOC6j3/84xk1alSuuOKKTJkyZaH99t5774wZMyallDrpLuSoo45Kknzxi8vWWACgMz358JRMuvHqDB42PLsd8g8LrXvzJ/9v1hg6LLdfcmGen73kUcZLcs/Vl+Xxhx7IO449NWuuv+Ey53T7JT/KC3NmZ9s3HZjh63Qv8/4AAACwsqh7U743tZ8vr6pq7oIrqqqakeS6JMOS7LaUOG9IMjTJde39/ppIV1fe9KbWYa655pqaab288847L5dccknOPPPMrLvusn31GYDONPnm3yVJ1lr/FenqWvgyNnj4iGz+mtflhTmzMvWOW2vFm/nk4/nxvx2ddTbcJDse+L5e5XTzj1tz9L/u3R/qcZs777wz3/jGN/LlL385F1xwQR555JFeHQsAAAD6U90pL17Vfv5jD+snpTWCeeskV/Q2zpgxY5IkkydPrplWz6ZOnZoTTjghhxxySN7+9rcvdzwAOsPjU1rXiCHDRy5xffeo0Zl049V5YurkvPL1ey813k8+d0yqam623GGXXuXz4B9uzp/vuyfrbT4mY3bds8ftvvWtby3082qrrZYPfehDOe200zJkyJBeHRsAAABWtLojlNdqPz/dw/p5y9denjhrrrlma+XTPR2mnrlz5+awww7L8OHDc/rppy9XLAA6y5yZzyRJBq2++hLXDxnRupbMmbH0a8ktPz0v91x9WQ46/gtZo5dN3Zt//P0kya7v+uAS12+++eY5/fTTc8stt+TRRx/Nvffem3POOSejRo3Kd7/73RxxxBG9Oi4AAAD0h7oN5aWZN7lxtTxBqqq1e2/mSl7Qf//3f+e6667LV7/61ay99tJ63AAMKO1rSZZyLXnq0an5xZc+k+3f/M7ssP/BvTrUnBnP5I5f/+xlb8a355575uMf/3he+cpXZtiwYdlwww1z8MEH5+c//3nWXnvtXHTRRbnzzjt7dXwAAABY0eo2lOcN81qrh/VrLrJdr+LMmNGaVnneSOXemDx5cr75zW/m0EMPzf7779/rOAB0pnkjkF984YUlrp/z7IyFtuvJReOPyuqDh+ag43v/TZbbL70wL8yZ1aub8W266abzr1PXX399r3MAAACAFanuHMoT289b97B+q/ZzT3Ms14ozb+7keXMp98aECRPy/PPP57zzzst55523xG122mmnJMm5555rfmWAlcz6W7SuEfMax4uaPvX+JMl6o17+WvLovXdkzsxn8rn9tpm/7Maf/XD+v6/6ry/nqv/6csbu87Z88MzvLzHGzT/5QZLk9e/58BLXT5w4IUeedGqPOdzxx9Z174KLL8ldj0x/2XyTpHvEkIw/7uilbgcAAAB9pW5D+ar28/6llK6qqubOW1FKGZlkjySzk9y4lDg3trfbo5Qysqqq+d2AuXPn5sorr0yS7L330m+i1JNRo0bloIMOWuIo58svvzzTpk3LwQcfnJEjR2bUqFG9Pg4A/WP0Lq0b3z39+LTMnTs3XV1//bLNc8/OzIN/uCmrDxmaUTvs/LJxdnz7IXlhzuz5Pz942/XZfKfdM33q/Xngthuy0au2yyavfk02ftX2S9x/6p235k9/vDvrbT4mo3fZY4nbdA0elrHjju0xh99e3bq8bvPOD2ZsjWk37jnnjKVuAwAAAH2pVkO5qqrJpZTLk+yf5PAk/7HA6lOSDE9yVlVVz85bWErZpr3vvQvEmVlK+UGSjycZn+SYeevOPvvsTJ06Nfvtt1+22GKLXp/QDjvskM985jPZaqutFlt34IEHZtq0aTnppJMyevToXh8DgP7TvdmW2Wq3fTLpxqtz44/+K7v/7cfmr/v1t76Q52fPyuve8+GsMXT4/OWPPTApSbLBln+9NrzzuNMWinvx+CNy0Elfya0/Oz8P3HZDttnzzdn/8BN7zGPezfhe9+4PvWy+D9x2Q7bc6Q0LLauqKr/97lcz9Y6bM3zt7my9+35LOWsAAADoDHVHKCfJp5Jcn+TfSyn7JZmQ5PVJ9k1rqot/WWT7Ce3nRe+KdGKSfZIcXUp5bZKbkrw6SdZff/188YtfXOzAv/jFL3LJJZckSR577LEkyU033ZTDDjssSdLd3Z3Pfe5zy3AqAKzMDjrh9Hz1fXvl56efmMk3/S7rb7lVHrrzttx/y7VZb/MxizWCv/ye3ZMkp932eCPHnzNzRu64/KdZbfU1stPb/+Zltz37o+/MepuPyaZjd8yaG2yUOTOfyYN/uCnT7puQ1YcMyyGf/2aGjBjZSF4AAADQ12o3lNujlHdJ8tkkb01yQJI/Jfn3JKdUVfVkzTjTSylvSHJykoOT7JVk+qGHHpoTTzwxm2yyyWL73HnnnTn//PMXWjZlypRMmTIlSbLZZptpKAOsQro32zLbvXH/dA0Znj/ecGUmXvubjFzvFdn9/R/Lfh8/NsPWWqdPj//7yy7K87NnZYe3vGupN+Pb64OH5+G7b8vkm3+X2c/8JaWrK2tvuEl2O+Qj2esDh2XdTbfo01wBAACgScsyQjlVVT2U5O9rbrvoyOQF1z2Z5Kj2I0ny9NNPVz1tf8IJJ+SEE05YhkyXbN4oZwBWfoOHDstB4/9j6Rtm2UYm7/zO92fnd77/ZbfZ7X1/n93eV+tymAP+aXztYwMAAECn61r6JgAAAAAAsIwjlAGA/jNx4oQcedKpjcXrHjEk4487urF4AAAADHwaygCwkugaPCxjxx3bWLx7zjmjsVgAAACsGkx5AQAAAABALUYoA8AqqrdTaMyaPTvDhg5d4jrTaAAAAAxsGsoAsIpqegqNxDQaAAAAA50pLwAAAAAAqEVDGQAAAACAWjSUAQAAAACoRUMZAAAAAIBaNJQBAAAAAKhlUH8n0AnWXnvt1j/+/fRG4974sx92dLy+iNnp8foiZqfH64uYnR6vL2Kuijl22jmfdtvjDWYCAAAA9IYRygAAAAAA1GKEMgDQscaffmamz5zTaMzuEUMy/rijG4tXN8dZs2dn2NChS92u6fwAAACapKEMAHSs6TPnZOy4YxuNec85ZzQar+kcm84PAACgSRrKSf7yl7/kyJNObfTD4MXjj8hB47/WsfH6Imanx+uLmJ0ery9idnq8voi5Kua4MpwzDFQTJ07IkSed2mhMo54BAICmaCgDAI1puhk65aGHMraxaCuHrsHDOn5UNgAAsOrSUAYAGtN0M3TS+CMaizWPpjcAAEDvlaqq+juHnHLKKf2fBAAAq6yTTz659HcOAACwMujq7wQAAAAAAFg5aCgDAAAAAFBLR0x50bRTTjml8rXF3lG73lO73lO73lO73lO73lO73lG33lM7AADoHAN1hPIp/Z3ASkztek/tek/tek/tek/tek/tekfdek/tAACgQwzIEcoAAAAAADRvoI5QBgAAAACgYRrKAAAAAADUoqEMAAAAAEAtGsoAAAAAANSyUjSUSymbllK+U0p5tJTyXCllSinlK6WUdZYxzrrt/aa04zzajrtpX+Xe35qoXSnlzaWUL5VSriilPFlKqUop1/Zl3v1teetWShleSjm0lPLfpZR7SynPllJmlFJuKaUcU0pZo6/Pob809Jo7tpRyaXvfmaWUZ0opd5ZSzvT7uswx9y6lvNT+vf1ck/l2koZed1e369TTY0hfnkN/afJ1V0rZvpTy/VLKQ+1Yj5VSfltK+VBf5N7fGrhW7LOU19y8x2Z9fS4rWoP/t9uzlHJxe/85pZSp7evHW/sqdwAAWNWVqqr6O4eXVUoZk+T6JBskuTjJvUlel2TfJBOT7FFV1fQacbrbcbZOcmWSm5Nsk+SgJI8leUNVVff3xTn0lwZr99O06jQnyX1JtktyXVVVe/ZR6v2qibq1P8heluTJJFelVbd1k7wjyYbt+PtVVTWnj06jXzT4mrsvycwkf0gyLcnqSXZM8sYkzyTZp6qq2/viHPpLU7VbJObIJHckWS/JiCSfr6rqM03m3QkafN1dndZr7JQeNvlcVVUvNpFzp2jydVdKGZfk20lmJflFkilJ1k7rmvFoVVV/23D6/aqha8UWScb1sHr7JO9OcndVVds1knSHaPB39rAk30jybJKfJHk4yaZp1W1Yks9UVfX5vjgHAABYpVVV1dGPJL9KUiU5cpHlZ7aXf6tmnLPa25+5yPJPt5f/sr/PtYNr94Yk2yZZLckW7X2v7e/z6+S6JXltkkOTrLHI8pFJbm3HOaa/z7UTa9fefkgPyz/WjnNpf59rp9ZukX2/k9YfNU5sx/hcf59nJ9cuydWty2L/n9NKWLvdkryY5PdJNlzC+tX7+1w7tXYvE//8dpxP9/e5dmLt0vpD41+SzE7yqkXWvTqtP4LPSjK4v8/Xw8PDw8PDw8PDY6A9OnqEcilldJLJaY1yGlNV1dwF1o1M8qckJckGVVU9+zJxhid5PMncJBtVVTVjgXVd7WNs0T7GgBil3FTtlhB3iyQPZICOUO6rui1yjL9Lcl6SX1RV9Y7lTrpDrKDarZVWA+G+qqq2Wu6kO0Rf1K6UclCSnyb5YJJBSb6bAThCucnazRuhXFVV6bOEO0jDtbsmyV5Jtq+q6q4+S7pD9PX7XftbVY+k9f+WTaqqeqqJvDtBg/+3e0WSPye5o6qq1yxh/R1pjfJer1rGb3cAAAAvr9PnUH5T+/nyBT9wJEm7KXxdWl9p3G0pcd6QZGhaTdAZC65ox728/eO+y51x52iqdquaFVG3F9rPA+qr81kxtZvXgL9jOWJ0okZrV0rZIMl/JvlpVVXnNploB2r8dVdK+ZtSyvGllKNLKW8rpQxuLt2O0kjt2vOa75XkliR3l1L2LaX8c2nNF79f+w+3A01fv9+NSzI4yYUDqZnc1lTtHktrsMDWpZSF/sBYStk6yVZJfq+ZDAAAzev0D3mvaj//sYf1k9rPW6+gOCuTVfGcm7Ai6vaR9vMvlyNGJ2q8dqWUj5ZSxpdSvlhK+VWS7yV5MMnxvU+zIzVdu7PTen//5PIktZLoi9/ZC5KcluRLSS5NMrWU8t7epdfRmqrdrgtsf2X7cUaSLyb5TZLfl1JeuRx5dqK+vlZ8tP18Vi/372SN1K5qfcXu8LTe624tpXyvlHJaKeX7aU0tdXeS9zWQLwAAsIhB/Z3AUqzVfn66h/Xzlq+9guKsTFbFc25Cn9atlHJEkremNc/od3oTo4P1Re0+muT1C/x8c5K/q6rqvmXMrdM1VrtSykfSuonm31RVNa2B3Dpdk6+7i9Nqgt6eZHqSzZN8OMkxSX5YSnl7VVWXLUeunaap2m3Qfj4kyRNp3RDtiiTrJzk5rWlXLimlbF9V1fO9T7ej9Nm1opTyxrRuGnx3VVXX9yK3TtdY7aqqurCU8mha801/aIFV09Ka5mdATGMGAACdptNHKC/NvHkul3ci6KbirExWxXNuQq/rVkp5d5KvpDXn43uqqnphKbsMNMtcu6qqdmvPZ7tekv3bi28tpby16eQ6XK3atec4/0paX5P/UR/ntLKo/bqrqurLVVX9oqqqR6qqmlNV1cSqqk5Mq6HcleTUvky0A9Wt3WoLPH+0qqqfVFX1TFVVk9NqyN+S1mjT9/RNmh1pea6xH28/D8TRyXXUrl0p5QNpjYL/XVo34hvWfr4iydfS+rYBAADQsE5vKM8bpbJWD+vXXGS7vo6zMlkVz7kJfVK3UsrBaX2wfSzJPgPl5o+L6LPXXFVV06uq+nVaTeXZSb5fShm67Cl2rKZq95206vOpJpJaSayI97pvpzXn+WvbNw0bKJqq3bw5fp9La4qQ+drTElzc/vF1y5pgB+ura8W6aTXeZyf5Qe9S63iN1K49T/J30pra4oNVVd1bVdXsqqruTWtU/K1J3ldK2Wf5UwYAABbU6Q3lie3nnubRm3cTlp7m4Ws6zspkVTznJjRet1LK+5JcmNZXcN9YVdXEpeyysurz11xVVX9JckNaX6XftrdxOlBTtdsprekHHi+lVPMeaX31O0n+pb3sp8uXbkdZEa+7OUnm3dB1eG/jdKCmr7EzFr3JWtu8hvNA+iNQX73uPpzWzfh+1H6/G4iaqt3+SVZP8tsl3NxvbpJr2j/u3JskAQCAnnX6HMpXtZ/3L6V0LfiBoT1KbI+0RvHcuJQ4N7a326OUMrJ9F/F5cbry16/SX7WknVdSTdVuVdNo3Uopf5fk+0keSbLvAB2ZPM+Kes1t0n5+cTnjdJKmavf9tL7yvaitkuyd1tzdt6Y1R/BA0eevu1LKq5Ksk1ZT+YnlyLXTNFW7O9Kqy3qllFcsYe7u7drPU5Y/5Y7RV6+7j7Wfz17+FO+c+CgAAANYSURBVDtWU7Ub3H5ev4f185YPlHm7AQCgY3T0COX2/IuXJ9kirTt5L+iUtEaKfb+qqmfnLSylbFNK2WaRODPT+uro8CTjF4lzRDv+rwZSs6+p2q1qmqxbKeXDab3upibZeyC9vpakqdqVUjYvpYxe0jFKKZ9IsmuSh5Lc2Vz2/avB97pPV1X10UUf+esI5Uvay77eZyezgjX4uhtdStlkkf1TSlkvf63fBVVVDZg/ZDT4unsxf53v9/T2H2rnbb99knFp/QHoooZPod/0xTW2lLJXWvP/3jVAb8aXpNHa/a79/N5Syg4LriilvDbJe9Oah/nK5rIHAACSpLSmN+xcpZQxSa5P62vcFyeZkOT1SfZN6+uQu1dVNX2B7askad/Ia8E43e04W6f14eKmtD64HZTWvLa7tz/kDBgN1m7PJB9t/zgirfkdH0ty2bxtqqoa11fnsaI1UbdSyr5p3SioK605Hh9awqH+UlXVV/roNPpFQ7U7OMmP23H+mNZUId1JdkuyfZKZSd5eVdVvV8AprTBN/b72EHtcWk3Rz1dV9ZnGk+9nDb3uxqU1V/Jvk0xO8mSSUUkOSGuu11uSvHmgTUPQ4HViWFo3QtstrRHwV6c1QvQ9aU11cUxVVWf28emsUE3/zpZSfpDkA0k+XVXVf/Rt9v2rwdfdd5L8fVqjkH+S5MG0GtUHJ1kjyVeqqvqnPj4dAABY5XR8QzlJSimbJflskrem1Vj6U5KfJjmlqqonF9m2xw9s7ZvdnJzWB42NkkxPqyl6UlVVD/flOfSXJmq3QDOqR3WaWiuT5a1bnZolebCqqi2ay7ozNFC7UUmOSrJXks2TrJtkTpL7k/w6yVerqlpSg36l19R73RLijssAbignjbzutk9yTFrzrW6c1o3BZqR1w68fJTmrqqoB+dX5Bq+xw5Icl+Rvk2yZ1u/tzUm+VFXVZYtuPxA0WLt1kjya1ojajQfaHy6WpKH/n5S05p0el+Q1SUYmeSatP2r8Z1VVF/TtWQAAwKpppWgoAwAAAADQ/zp6DmUAAAAAADqHhjIAAAAAALVoKAMAAAAAUIuGMgAAAAAAtWgoAwAAAABQi4YyAAAAAAC1aCgDAAAAAFCLhjIAAAAAALVoKAMAAAAAUMv/B0IvYBrd0EYMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.plot_posterior(trace, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 95% HPD is the same idea as a 95% confidence interval in frequentist statistics. In Bayesian stats, this is called the Highest Posterior Density."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Traceplot\n",
    "\n",
    "The traceplot shows a kernel density estimate and all the samples that were drawn on the right. We collapse the chains on th plots (`combined = True`) but in reality we drew 2 independent chains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\willk\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py:3604: MatplotlibDeprecationWarning: \n",
      "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
      "  alternative='`bottom`', obj_type='argument')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prop_cycle = plt.rcParams['axes.prop_cycle']\n",
    "cs = [x['color'] for x in list(prop_cycle)]\n",
    "\n",
    "ax = pm.traceplot(trace, varnames = ['parameters'], figsize = (20, 10), combined = True, skip_first = 1000);\n",
    "ax[0][0].set_title('KDE of Posteriors'); ax[0][1].set_title('Values in Trace');\n",
    "add_legend(ax[0][0])\n",
    "add_legend(ax[0][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum A Posteriori Result with PyMC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "logp = -1.8042, ||grad|| = 1.118: 100%|██████████| 7/7 [00:00<00:00, 878.23it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Species: lions    Prevalence: 50.00%.\n",
      "Species: tigers   Prevalence: 33.33%.\n",
      "Species: bears    Prevalence: 16.67%.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    # Find the maximum a posteriori estimate\n",
    "    map_ = pm.find_MAP()\n",
    "    \n",
    "display_probs(dict(zip(animals, map_['parameters'])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MAP estimates are exactly the same as the observations. These are also the results that a frequentist would come up with! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sample From Posterior\n",
    "\n",
    "We can now use the posterior (contained in the `trace`) to draw samples of data. For example, we can simulate 1000 trips to the wildlife preserve as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:02<00:00, 476.68it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'lions': 2.605, 'tigers': 2.021, 'bears': 1.374}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with model:\n",
    "    samples = pm.sample_ppc(trace, samples = 1000)\n",
    "    \n",
    "dict(zip(animals, samples['observed_data'].mean(axis = 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These represent the estimate number of each species we'd see over 1000 trips to the preserve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fD+nvb3q+/hTLay5zusvrWWb+hvJjvH771IaUW2s+CfwQuD3KoD6fjWpQn6nKcnvTf1dP16bcVtXNlzLzljbl3U/5Qmq4NDN/2KGs79ce91Kn0zPz/HYrM/PrlNvUoFzRu7Bd2g5ezWS3EZ/NzNu6pP93yhcslNud6urfd9N760x/FlKCNpSztF9sl7B6rz9XW/S3PZTfy614q1r9lqkPZOYjHdIeWnv8iug+SOSnM/OPHdZ/u/a41a2os/U40egz7rZh3AWMu6vSXIy7da+i9BMKcFpm/r92CTPzZEpjdid7Um7ZhvKHuWP6zDyNyeP0JV33tvvrOVuPM40GY3MbxmbA2LwqjXJsPjoz7+qw/p8pJ5gB9mkx6OTfMxmXP56Z3T7r9e7Amt/fnmXmzykN7DDZ9Wc3H8uqVbuDxjE248eXDd5z1zq1x8t6SN88uvQ6HZ73Ul5zmdNdXl+qoPVESmPbNW2SPZ7SZ9cVEfFfVX+IXUUZVfnFEfGWapTg/9OYWLEB7ok9FHd6l/XX1x6f0UfaLXrY9qk9pPlO7XFfoxNX6j8IutWVzHyY0mczwI5NI/7+ovb43RGxF7NDfXTkb2f3ft1Oqj3+qy5pf139WJ01IuIvgD+vnv4eOK9T+sy8jsk+A9eg9DnWyY+7rP917fFmLdZfWXv8pYjo5bMg9cK424Fx17i7Cs2puNvCs2qP/28P6bul6euYqTRi7aMjYpsO6bq+npl5B5MNcgsj4m1VX6hSL4zNHRibjc2r0CjH5o7HQGbeTBnXAsr/2V2akvT7/v6O8j8aJvuobyki5kXE0yLiNRFxYES8u+mztmaV9LHVmAGd3E+X/+6VRox/fER8MiKm9D00Ff4YmLseqD1es22qSc0H/wMdnvdSXnOZ011e3zLzHuAo4KiIeCzwbMoXyk6UvsfqZ+ZeAzw5Inav8q0kIl5HGUyj17PfG/WQ5sYu6++tPe4nbberaGHFhsF26gH1CT2kb7ZD7fHPIqJtwhZWpwzKcCdAZl4bEd8F/qZafnZE/Br4EaXPrQuyt0FRhq3+ulzRQ/prKD9416QEpjUzs90P4GununPToF7fK3s4QwxlsI2dq8ePB87pkPa3Xcqqfz6bz65DuZrgIGADyq2aN0XEeZRBbS4EfpaZzX92pF4Yd7sw7nZl3B2OuRZ3m82vPf5lD+m7pakfMydFxEltU7b2aNrH7l5fz6MoV7w1+uv9SET8kNKP6IWZ+atOmTWnGZu7MDZ3ZWwejlGNzQ+y4gVV7fyCyQu3nsCKdx3U39/b+3x/H91qYURsBHyYcvX7pq3StLARpT/6dq7rcmd2w1FM3lX9fuCtEfFjSmP5hcAvejihMRRe4T139ftFvm7T8+YA1m95zWVOd3lTkpk3ZuY3M/M9mflcyijIL2HFUYWfyoqj0wMQEatFxFeBE+g9sENvt4B0a3irNyb2k7aX74Y/9JDmztrjjXtI36zXL+d2mo+dNzB5ixyUYPP2atnvIuKaiPjniHjUFLfbj/qPuDvbpqpUQaY+4nun13XpoDs1jfqqb+X3tcebdErYQ2N0x+M8M39LaehuXN0xj3LW/ROUHyZLIuJHEfGqiDCGqh/G3T4Yd1sy7g7HXIu7zer17+WY6pZm2MdMXU+vZ2Z+FvgIZZAzKA0AbwT+A7gmIm6NiOMi4slT2lONI2NzH4zNLRmbh2NUY/PdPTbetjwGImINptD1EC2+FyJiO8oFY4fQ37HT7bPWa0w+ldJNS6Ob0Q0og6keSzmZcWdE/GdEDHK3Q1+8wnvuqp+52bJtqklb1R4vaXH2rN/ymsu8fZrLG6rqNqHTIuJHlFs9X1StenNEvDcz/1RL/mbggOrxw5Qf39+nnGm8A3ig8SUZEW8CvjKd+76K9XV6soX67Vcfof+rFOpBsHGFwqsj4pPA64C9KFcnNL4L/5IyaMghEXFA9WW9KvVytXM/eVbJmdMpGHZ9hyIzL46IJ1GufPgbYA/gsdXqtYDnV9P/i4h9ZugqCI0e4+4UGHd7Ztztz1yLu9D/MdItff2YORr4XZ/lX99hXc+vZ2Z+PCK+DOwP7E25CrXRELAFcCDwjxFxeGZ+qM991PgyNk+Bsblnxub+jGNsbncM1N/bBylXZU/V14FGd2GLKQ3N51Puplpav0CsupN5jx7L7ScmfykiTgFeS7mY7K+YbOjfmHLS5Q0RsQj4+6bviqGxwXvuuobSkAMr3trYzuNqj1sNRlPv06treRGxKWXQC4BHWPk2k2spH6jVgI0jYtPM7Hb2tNs+Dl1mPhIRH2AyuG9A6Wesvv2Da49fkZmd+kLsqc+zWaKXs4X1NHe3TdXeXcDm1eNTMrNd33F9ycwrqW4/izII4m7AC4HXU/p13gD4ZkTsNKxtdlB/XbqeRa/6YKufwV4y9D2aXn3Vt0W6QY6jvlU/4E+uJqpbOPcE9gVeSvlx8gzKlRC9DvKhuc24OwTG3b7SGHdbm2txt1m9/r0cUx3vrKIcMw1nZuYP+t+l4aj6Nf0U8KmqH++dgOdSGsGfTPl++2BELM7ML83UfmpWMTYPgbG5rzTG5tZGNTZvHBGr9XCVd8tjIDMfjIgHKP3trw0c38OglW1FxM5M9od+A7BzZnZ6babts5aZdwPHAcdF6aflKZQ7p19D6Q4JykmwW4BpORHt7dhzV71fpN3bpppUHwigVZ9KP2fyrNr2VZ9BvZb3q8x8qL6yOutUD/gd9zEiNmZyhPjl9NaX1rA09wv4v18aEbEu5bYugOu7BHYoP8ZHxQ7dk/xv3aG3vq2a1V/bXo7TvmXmfZl5Zma+m/ID8WfVqjUpt+JMt4na415u7/tLJvvw+22Hvspmq3p9n9ZjnvrrMtE21TSqbuH8z8zcF1jA5G3TfxURvdZDc5txd3iMu+0Zd7uba3G3Wb3+T+khfbc0037MDCIz/5SZl2Tm4ZTPxedrq986Q7ul2cfYPDzG5vaMzd2Namxem95OlnU6Burv77OnuD/1gam/2qmxu+pOZZA+5fuWxVWZ+dnMfBalH/+GA6erq1AbvOeuHzHZYLNjRDyuXcLq4Nu3tug7zWmyjJD+0+rpasDLu2z/FZ3Kq3y3TfpWXs7k8XxRZv6+U+Ih27zpef2se/2s4110EBFrUa4cHRX7dk/CPrXHFw+wjfoo2m8aIH9fMvNeyu24DU+a7m1SBm5o2De6j1LxyjZ5R0JmXg80ugDZLCI6Xh0dEX/B5ICVD7NiH4EzIjMvZMWBM1fFcaLRZ9wdHuNue8bd7kYt7j7ceFBd0TZVP609flkP6bulqR8z+1d/oGeVzEzKWBwNxm01GJuHx9jcnrG5u1GLzXUdj4GI2BLYtXr6MHBpU5Jhvr89f9Yod2SsM8XtDeozQONK9k1oM/jmVNngPUdV/TY1gmcAH+yQ/A1M9gF0E2V01Va+Xnv8nipYrSQinsDkF9Ry4MQ25Z3A5BnyV1X5WpW3NvB/2uxH3yJi7x6+YOveUnv8B+C62vO7mazDX0ZEpy+U97HyD4XZ7HkR0fYMc0TsT7mVDUoD51kDbONEJm/52S0i3tIpcdP2p9pXGgxhZPMenEW5jQfg8cDftUsYEVtQBhRp+No07td0+s/a43/pckb3k0z2eXbyVG7xmkar4jjRiDPutmfc7ZlxdzhGLe7+sfa4W/civfgWk43oL4qIXdsljIhX0P1KyzOYvDJvG+Cfe92RIR0zgzBuCzA2d2Js7pmxeThGLTbXvavL3RyHMdn2+p3qhELdvwGNPqxfHRHP73XDLd7f+ommnWmj+gx+stftTIPVWLFP8Gk5xmzwnts+wuQH600R8Y7mBBGxB/C52qIPdehQ/stMDjzzJGBRc4Cvzm6dQhn4DeBrmdl8+xMAmXk1JcBTpT+5yl8vby1gEZNnHSeY+gAXXwd+GRFvj4i2wTYi1oiI97LiD6OvVCMGN+pwP3BZ9fTPKP0XrVlLT0SsHhHvofxBmPYB+Ybs5IhY6ZajiHgu8MXaoqMGGYggM//IigM3HB8Rh3b44RgRsVtEfI0VgyAR8d6I+GLVr1VLEfEYVnw/L+h3n/tVvS71q46OjYh9mtNFxNbAD5gcwfoiVjwbPEo+x2Q/a3sAX27+4RsR8yLiCODV1aJlwOHTvWMRcVb12d+sQ5p9KQNiQfkO/Wm7tFIT425rxt3eGXenaATj7v/UHi+YamHVFahfrZ6uBnw7IlbqtiQiFlC+Yzp+RqrP3yG1dB+MiM9ExPrt8kTEDhHxOeCIAarQXNYeEXFaRLww2lxdXjUEfqa2aNqPM40UY3NrxubeGZunaARjc0NS+jv/vxGxwlXK1ftwKJMngx4BjlypgMwbgM9WTxtx+e+izV1d1f/k50bEd1j56vLza4//NiJe1LS+ccLgNEr3R0P9rEXENhFxfkS8svn/fS3N6pT3uvE74arqGB86B60cIdUH6PguyY6LiPublh3Y6namzPyfKqg0blf5bES8gfKF8RDwdMptDo0TI9+iw5nizFwWEa+nnJ1bh9IZ/V9FxLeB31PO1O0HrFdl+TUr9t3TyiGUfogeT+n36Nooo71eR7nt4eVMjkR9P/CGIY3wuj1wDHB0RFxNue3kd8A91f4/njIITn1AhZ8DH2tR1pGU1w5Kp/wLIuKHlDOYW1AGhnh8tf9fpNR5FBwDvBO4JCJOAy6nDOT3bMpgBI2zjeex4g/EvmTmFyLiycCBlO+sIygjRp8O/IZyrG5IOXP+TODPq6xXNRW1LvCPwD9GxI2UfskmKO/pxpQfiC9gsi+wG4B/H3S/+5GZx0fE8yi3u60NnBoRF1Feu/spfZT9DeUHIpTP0+urW3RHTmb+LsqVCSdRjpkDKFdHfBe4mfLZfikrDrrz7sxsfk+nw+Mox/ZnIuIySv+Mt1L+CG1OaWyo99V3dNV4oDFk3DXuzjLG3SEZsbj7A+C11eMvR8SelM9j43N3S2ae2meZh1JO3G5H+TxfHhHfp3ymVqd8B+xNOaY+Dby7ytey/pn5/Yh4H5N/5N8F/F1EnEHpf/g+yuBnj6MM+Lxtle4Lfe53K6tRvjdfBNwdET+lDBx4F+V78bGU3xSN27yX0cdV6Jp9jM3G5lnG2DwkIxabG26kvOf7Ar+OiFMpn8uNKMd0/YTy4Zl52cpFAOXOhidS4tW6lBNn/xwRZwK/pcT8Rh/9z2RyEMxv1AvJzKur4/DFlOPwtKqMyyixePtqG38GnEs5lupjCUxVVOX9FXBfFZN/SXmv1gC2rPatcXwm8IEhbn9Fmek0IhPlx2EOMG3bpdxDgAe7lPE1YK0e9/O5lAaiTuX9DNimx/K2A/5fl/J+BzxnSK/zf/XwetSn5ZQuGjbsUObHupRxJ/B8SvBvLDusTVnn9vHeHlZLe0CXtHvW0i7qZduUH4ad6nUmsP6Q9u9tlKuCe3lP7qGM/l3P/4E+3tNLez0+e/y8nttD+jUoPyaWd9m3q4D5U3kfp1ivxY3yO6RpbH9xl7L2odx21am+9wJvmeo+9fr6UP509HKMPEJpBFht2K+x0+yZMO52Ks+42zrtYbW0B3RJ2/H7qNW2Me72+nk9t4f0oxJ351Gurmu3f+c2pe/pPa5er2s6lPsw8A5Kg01j2XFd9vUVwG09vucPAe+Y6utJGcCt1+PsVuC5w36PnFbthLG5U3nG5tZpD6ulPaBL2q7fQc3bxtjc6+f13B7Sj0psbpS9mNK4fU6Xz8aneihzteoz8kCP788fgN1blLMppRG+U95zKCfLVjiWh/D+bU35n9zL/i8F9h/2e1OfvMJbZOZnqqs6/oFyNm8ryhm931EGAPhqZp7bR3lnRsT2lNF896Gcqd0QuAP4BfBN4MSs3ebUpbwbImI3YH/KGfKnUm4bWUo5e3Yq8KXMvLt9Kb3LzNdWt2HuRTkztVNVh0dTzjTeT7lq5FeUW2hOysyOoy1n5kci4izgYMrZ3kdV+38j8H+Bf8/MWyPigGHUYVXJzHdFxA8ox84zKGfn/0i5KnYR8F9ZffMNYVvHRsTXKT+A9qZcZfsoyh/BpZRbB39O+UHxg2zq6zkzPxkRP6ry7kY5Q/wYyhnUByhXF1xOufLgO5lZ71Nq2mXmw8A/RMS/AW+mHH+Pody6+Psdhib9AAAgAElEQVRq304BTuj1szPbZeZ3IuJcylUGL6ac1d6Ycgz9hjKQ0Bcz89a2hQzfjpQ/93sBu1CuRtuUcob8j5QrIM6nfC9eswr3S2PEuLvS9oy7PTLuDs+oxN3M/FNELKRc1bcv5eqsjZjinbqZubi6Bf+fKJ/zJ1GuRr2FcjXdcZl5WUTUB91b2qXMk6vvttdTvtt2ZvJz/EfKVWq/AM4Gvp+Z3QbU6qUeF0bENpQr6f6K8n31WMoV5Q9TGtCuoty+/Z9Z+myWVmJsXml7xuYeGZuHZ1Ric11mLqm6rzmA8vncnvKf9g7K/8ZjM/OiHspZDnwkIo6jDF65kPL+NK7mXkL5rF8OnA6cnpnLWpTzh4h4NuU/9muq/VkbuJ0SD0+kHJPLY8hDaWTmTRHx55SY/NfA0yiN5htSGrnvAq6u9v+rOc0D68aQPneS5oCqcXJB9XS7zFw8c3sjSdJ4M+5qpkXEB4F/qZ4emJlf7JReksadsVkaDQ5aKUmSJElqpT7gVbu+RyVJkmYVG7wlSZIkSSuIiBdSuh0AuAkbvCVJ0oiwwVuSJEmS5pCIOCwi9oo2HXhGxEspg9Y1fGFV9+UqSZI0KAetHJKlS5faGbrG3u67786FF14IwJVXXnnD0qUdxy6SNAQbbrjhcEcTmSOMyxoHxl1NlwULFnDeeeex9dZb89rXvpZtttmGtdZai9tvv50LLrhghbQ777wzp59++hFLly49YoZ2d9YxNg/G2KxxYGyWZp9WcdkGb0mSJEmag2666Sa++c1vtl2/cOFCvvKVrzBvnn8bJUnS6PCXiyRJkiTNIccddxxnnnkmZ599NhMTE9x5553cfffdrLPOOmy++eY885nPZL/99mOvvfaa6V2VJEnqW2R6V9EwzNTtWRMTE8yfP38mNr1KWc/xYj3Hx1yoI8xsPb1tejDG5ellPceL9Rwv1nP6GZsHY2yeXnOhnnOhjmA9x431nH6t4rKDVkqSJEmSJEmSxoIN3pIkSZIkSZKksWCDtyRJkiRJkiRpLNjgLUmSJEmSJEkaCzZ4S5IkSZIkSZLGgg3ekiRJkiRJkqSxMKsbvCNijYhYGBGfjoifRsStEbEsIm6JiJMjYs82+RZFRHaYru2wzdUi4q0RcWlE3BsRSyPi/Ih47bRVVJIkSZIkSZI0ZfNmege6WACcUT2+DbgMuA/YHtgP2C8iPp6ZH2mT/0LguhbLb22VOCJWB74NvAz4I3A6sBawEDgxInbLzLcPWBdJkiRJkiRJ0jSa7Q3ey4FTgGMy8/z6ioh4NXAC8OGIOCczz2mR/0uZuaiP7b2T0th9DfCczLy92tZ84Hzg4Ig4KzO/239VJEmSJEmSJEnTaVZ3aZKZZ2fmK5obu6t1JwGLqqevn+q2qqu731s9PbDR2F1tawI4tHr6waluS5IkSZIkSZI0fLO6wbsHV1TzrYZQ1m7AZsDNmfmTFuu/BTwM7BoRWw5he5IkSZIkSZKkIZrtXZp0M7+at+yTG9grInYA1gNuBy4AzsjM5S3S7lTNL2lVUGbeHxFXAztW0y0D77UkSZIkSZIkaehGtsE7IrYADqientIm2RtbLLsmIl6TmVc1Ld+umv+2w2ZvpDR2b9chjSRJkiRJkiRpBoxkg3dEzAO+AWwInJWZ32tK8nPgMuAsSgP2BsDOwCeApwFnRsTOmVm/Snu9an5fh03fW83X77R/ExMTvVRjaFb19maK9Rwv1nN8zIU6wqqt5/z587snkiRJkiRJKxnJBm/gi8BC4CZaDFiZmZ9tWnQfcFpEnAGcBzwLeD/wtlqaaGSf6s6tyoaKiYmJOdEwYj3Hi/UcH3OhjjB36ilJkiRJ0qgbuUErI+IY4M3AbcDCzLyt17yZuQw4vHr6oqbV91Tz9Wivse6eDmkkSZIkSZIkSTNgpBq8I+LTwNuB31Mauwe5v/zaar5l0/LF1XybDnm3bkorSZIkSZIkSZolRqbBOyKOAg4B/gDsnZnXDFjUptX83qbll1fzXdtsf13gKdXTKwbctiRJkiRJkiRpmoxEH94RcQTwHuBuSmP3lVMo7lXV/JKm5RcDdwBbRcQemfmTpvWvBNYALmka7FKakzbcaKOB8+4yYL6lS5YMvE1J0tw1aMwaNF6BMUvSqhMRBwN/DTwV2AzYAFgCXAksAk7IzJXGqoqI1YADgTcBTwIeAX4BHJeZ/9Vlm6+r8u4ArE65k/qrwPGZuXwoFavxv4ckqR+z/grviPg4cCglYO+dmR2vro6IHSPiJRGxetPyeRFxCKVLFICj6+sz8xHgU9XT4yNis1re+cAR1dNPDFwZSZIkSZKG61BgH+AB4CLgFOA64DnA14FTq8bt/1X9Xz4VOBaYD5wOXEC54/nEiPhcu41FxBeAEyhtyecDZwBPqMo6ufm/uCRJq9qsvsI7Il4GfKh6eh1wcES0SnptZjYapLelBO67IuLXwM3A+pSz3Y8BlgOHZuaPW5RzNLAH8FJgIiLOolzV/VxgbeDzmfndIVRNkiRJkqRheA1wRWbeV18YEU8GzgL+BvhbyhXYDe8EXgZcAzwnM2+v8synNGIfHBFnNf//jYj9gIOA24A9GuNqRcTmwDnAvsDbgGOGXUlJkno126/w3qT2eBdKkG41vaCW7kpKcP0f4LGUxusFwP2UAP+MzDyq1caqq7z3AQ6mNLA/v8p7GbB/Zr69VT5JkiRJkmZCZl7Q3NhdLb8a+EL1dO/G8uoK7PdWTw9sNHZXeSYoV4wDfLDF5t5fzQ9tNHZX+W6ndHEC8L7mK8olSVqVZvUV3pm5iNLnWD95bqCcrR50m8spt2IdO2gZkiRJkiTNAn+q5g/Wlu1G6ev75hZjVwF8C/gPYNeI2LIxhlVEbAU8HVhWpVlBZp4XEbcAWwLPonSvIknSKudZV0mSJEmSxkxEbAf8U/X0e7VVO1XzS1rly8z7gaurpzu2yHd1Zj7QZrOXNKWVJGmVm9VXeEuSJEmSpO4i4k2ULjnXALYCnk25yO3wzDy1lnS7av7bDsXdSGns3q62rNd89bSSJK1yNnhLkiRJkjT6dqeMcdXwJ+DDwGea0q1XzVfq97vm3mq+/hDyrWRiYqLT6pXs0lfq4eh3H2eDUdznfs2FOoL1HDfWc/jmz5/fcb0N3pIkSZIkjbjMfAvwlohYh3KF9ZuAw4BXRcSLMvN3VdJoZOlzE4PmW0m3horZYBT2sW5iYmLk9rlfc6GOYD3HjfWcGfbhLUmSJEnSmMjMBzLzmsx8D/B+4GnAsbUk91Tz9VbKPKmx7p7askHzSZK0StngLUmSJEnSePpqNX9pRKxRPV5czbfpkG/rprRTySdJ0ipllyaSJElz1IYbbTRQvqn0pbp0yZIp5JYk9WkJpS/vecAmwO3A5dW6XVtliIh1gadUT6+orWo8fnJErJOZD7TIvmtTWkmSVjmv8JYkST2JiDUiYmFEfDoifhoRt0bEsoi4JSJOjog92+RbFBHZYbq2wzZXi4i3RsSlEXFvRCyNiPMj4rXTVlFJksbHHpTG7iXAndWyi4E7gK0iYo8WeV4JrAFckpm3NBZm5k2UxvI1qzQriIgFwFbAbdU2JEmaEV7hLUmSerUAOKN6fBtwGXAfsD2wH7BfRHw8Mz/SJv+FwHUtlt/aKnFErA58G3gZ8EfgdGAtYCFwYkTslplvH7AukiSNvIj4a+CxwMmZ+VDTut2BL1dPv5yZjwBk5iMR8SngU8DxEbFXZt5R5ZkPHFHl+USLTR4OfAs4MiIuyszrqnybAcdVaY7IzOVDq6QkSX2ywVuSJPVqOXAKcExmnl9fERGvBk4APhwR52TmOS3yfykzF/WxvXdSGruvAZ6TmbdX25oPnA8cHBFnZeZ3+6+KJElj4XGUfrqPjYjLKSek16+Wb1+lOQ34cFO+oylXf78UmIiIsyhXdT8XWBv4fKv4mpknR8TxwIHAVRFxJvAw5WT0BsB3WHGATEmSVjm7NJEkST3JzLMz8xXNjd3VupOARdXT1091W9XV3e+tnh7YaOyutjUBHFo9/eBUtyVJ0gg7D/g48HPgCcDLgecBf0Y5Sb1vZr6kub/t6mrvfYCDKXdfPZ9yJ9dlwP6d7qDKzIOA/Sndmyyo8l4HvA3Yr3EluSRJM8UrvCVJ0rA0Bqjaaghl7QZsBtycmT9psf5bwH8Au0bElvU+RiVJmisy8wagXVdi3fIup1yN3fcV2Zl5InDiINuVJGm62eAtSZKGZX41b9knN7BXROwArAfcDlwAnNGmn8+dqvklrQrKzPsj4mpgx2qywVuSJEmSZIO3JEmauojYAjigenpKm2RvbLHsmoh4TWZe1bR8u2r+2w6bvZHS2L1dhzSSJEkjYcONNho47y4D5lu6ZMnA25Sk2coGb2nI/JEiaa6JiHnAN4ANgbMy83tNSX5O6RP0LEoD9gbAzsAngKcBZ0bEzk3dkqxXze/rsOl7q/n6nfZvYmKil2oMzare3lQMGnemYiZen7lSz6kYtf0dlPUcL6uynvPnz++eSJIkzQo2eEuSpKn6IrAQuIkWA1Zm5mebFt0HnBYRZ1AG23oW8H7KYFcN0cg+1Z1blY0UExMTNop0MVden1Gq51w5bq3neJkr9ZQkSf1bbaZ3QJIkja6IOAZ4M3AbsDAzb+s1b2YuAw6vnr6oafU91Xw92musu6dDGkmSJEnSHGKDtyRJGkhEfBp4O/B7SmP3IPeWX1vNt2xavriab9Mh79ZNaSVJkiRJc5wN3pIkqW8RcRRwCPAHYO/MvGbAojat5vc2Lb+8mu/aZvvrAk+pnl4x4LYlSZIkSWPGBm9JktSXiDgCeA9wN6Wx+8opFPeqan5J0/KLgTuArSJijxb5XgmsAVzSNNilJEmSJGkOs8FbkiT1LCI+DhwKLKE0dne8ujoidoyIl0TE6k3L50XEIZQuUQCOrq/PzEeAT1VPj4+IzWp55wNHVE8/MXBlJEmSJEljZ95M74AkSRoNEfEy4EPV0+uAgyOiVdJrM7PRIL0tcCpwV0T8GrgZWB94KvAYYDlwaGb+uEU5RwN7AC8FJiLiLMpV3c8F1gY+n5nfHULVJEmSJEljwgZvSZLUq01qj3epplbOY/IK7CuBY4BnUAag3AlISsP3V4EvZOZlrQrJzEciYh/gIOBNwPOBR4DLgOMy88Qp1UaSJEmSNHZs8JYkST3JzEXAoj7z3AC8cwrbXA4cW02SJEmSJHVkH96SJEmSJEmSpLFgg7ckSZIkSZIkaSzY4C1JkiRJkiRJGgs2eEuSJEmSJEmSxoIN3pIkSZIkSZKksWCDtyRJkiRJkiRpLNjgLUmSJEmSJEkaCzZ4S5IkSZIkSZLGgg3ekiRJkiRJkqSxYIO3JEmSJEmSJGks2OAtSZIkSZIkSRoLNnhLkiRJkiRJksaCDd6SJEmSJEmSpLFgg7ckSZIkSZIkaSzY4C1JkiRJkiRJGgs2eEuSJEmSJEmSxoIN3pIkSZIkSZKksWCDtyRJkiRJkiRpLNjgLUmSJEmSJEkaCzZ4S5IkSZIkSZLGgg3ekiRJkiRJkqSxYIO3JEmSJEmSJGks2OAtSZIkSZIkSRoLNnhLkiRJkiRJksaCDd6SJEmSJEmSpLFgg7ckSZIkSZIkaSzY4C1JkiRJkiRJGgs2eEuSJEmSJEmSxoIN3pIkSZIkSZKksWCDtyRJkiRJkiRpLNjgLUmSJEmSJEkaCzZ4S5IkSZIkSZLGgg3ekiRJkiRJkqSxYIO3JEmSJEmSJGks2OAtSZIkSZIkSRoLNnhLkiRJkiRJksaCDd6SJEmSJEmSpLFgg7ckSZIkSZIkaSzY4C1JkiRJkiRJGgs2eEuSJEmSNIIiYo2IWBgRn46In0bErRGxLCJuiYiTI2LPNvkWRUR2mK7tsM3VIuKtEXFpRNwbEUsj4vyIeO20VVSSpD7Mm+kdkCRJkiRJA1kAnFE9vg24DLgP2B7YD9gvIj6emR9pk/9C4LoWy29tlTgiVge+DbwM+CNwOrAWsBA4MSJ2y8y3D1gXSZKGwgZvSZIkSZJG03LgFOCYzDy/viIiXg2cAHw4Is7JzHNa5P9SZi7qY3vvpDR2XwM8JzNvr7Y1HzgfODgizsrM7/ZfFUmShsMuTSRJkiRJGkGZeXZmvqK5sbtadxKwqHr6+qluq7q6+73V0wMbjd3VtiaAQ6unH5zqtiRJmopZ3eA9aH9ktfyvq/oSW1r1LXZp1ddYx3pHxAsi4vSIuCsi7o+IX0bEByNiraFWUJIkSZKk6XNFNd9qCGXtBmwG3JyZP2mx/lvAw8CuEbHlELYnSdJAZnuXJgP3RxYRXwAOAh4EzqIE3oXAscDCiHhlZj7SIt97gSOBR4Bzgbur/fgX4CURsTAz7x9mJSVJkiRJmgbzq3nLPrmBvSJiB2A94HbgAuCMzFzeIu1O1fySVgVl5v0RcTWwYzXdMvBeS5I0BbO9wXug/sgiYj9KY/dtwB7V7VVExObAOcC+wNuAY5rK3AU4Arif0h/Zz6rl6wGnAXsAnwDeNfyqSpIkSZI0HBGxBXBA9fSUNsne2GLZNRHxmsy8qmn5dtX8tx02eyOlsXu7DmkkSZpWs7rBOzPPBs5us+6kiNgbeDOlP7L6ABzvr+aHNhq7qzy3R8SBlCu33xcRn286c/0+IIAjG43dVb57I+JNwARwUER8NDOXTL2GkiRJkiQNV0TMA74BbAiclZnfa0ryc8od1GdRGrA3AHamXOD1NODMiNg5M+tXaa9Xze/rsOl7q/n6nfZvYmKi0+qV7NJX6uHodx+HYa7UcypGbX8HZT3Hi/Ucvvnz53dcP6sbvHuwUn9kEbEV8HRgGaUPsRVk5nkRcQuwJfAs4KIq35rAC6tkJ7TId31EXAzsDrwIOHF41ZAkSZIkaWi+SOnS8yZaDFiZmZ9tWnQfcFpEnAGcR/mv/H7KndEN0cg+1Z3r1lAxG4zCPg7DKNVzYmJipPZ3UNZzvFjPmTGrB63sQav+yBr9il2dmQ+0yXdJU1qAJwLrAndl5m/6yCdJkiRJ0qwQEcdQ7oS+DViYmbf1mjczlwGHV09f1LT6nmq+Hu011t3TIY0kSdNqZBu8O/RH1mu/YvW09cc30l6rfJIkSZIkzbiI+DTwduD3lMbuQe4vv7aab9m0fHE136ZD3q2b0kqStMqNZJcmXfojG7RfsRnrj2yq7Atodpkr/a7NlXpO1Sjuc7/mQh1hdvVHJkmS1CwijgIOAf4A7J2Z1wxY1KbV/N6m5ZdX813bbH9d4CnV0ytapZEkaVUYyQZvOvdHNmi/YiPZH9ls6yNnusyVeg5qrrw2o1bPuXDczoU6wtyppyRJGk0RcQTwHuBuSmP3lVMo7lXV/JKm5RcDdwBbRcQemfmTpvWvBNYALmka7FKSpFVq5Lo06aE/skH7FbM/MkmSJEnSSImIjwOHAksojd0dr66OiB0j4iURsXrT8nkRcQilSxSAo+vrM/MR4FPV0+MjYrNa3vnAEdXTTwxcGUmShmCkrvDusT+yxdW8337FGo8f22c+SZIkSZJWuYh4GfCh6ul1wMER0SrptZnZaJDeFjgVuCsifg3cTOm286nAY4DlwKGZ+eMW5RwN7AG8FJiIiLMoV3U/F1gb+HxmfncIVZMkaWAj0+DdR39kjbPZT46IdTLzgRZpdm1KC2VgjgeATSLicZn5mxb5ntEinyRJkiRJM2GT2uNdaD/UznlMXoF9JXAM5f/tNsBOlK49bwa+CnwhMy9rVUhmPhIR+wAHAW8Cng88AlwGHJeZJ06pNpIkDcFINHj30x9ZZt4UEZcDO1P6EPvPprIWAFtRukS5uJZvWUT8EHg5sD/wsaZ8fwHsBiwDThtCtSRJkiRJGlhmLgIW9ZnnBuCdU9jmcuDYapIkadaZ9X1499sfWeXwan5kRDy+VtZmwHHV0yOqQF13BOXM9qER8YxavvWAr1Ber+Myc8lAlZEkSZIkSZIkTZtZfYX3gP2RkZknR8TxwIHAVRFxJvAwsBDYAPgOLc5GZ+YlEfE+4Ejgoog4m9LQvgDYDPgZ8MEhVU+SJEmSJEmSNESzusGbwfojAyAzD4qIC4C3UhqsV6f00/0V4PgWV3c38h0VEb8A3k3p63tt4Hrgc8C/ZuZDg1dHkiRJkiRJkjRdZnWD9yD9kTXlPxHoe9CMzPwR8KNBtytJkiRJkiRJWvVmfR/ekiRJkiRJkiT1wgZvSZIkSZIkSdJYsMFbkiT1JCLWiIiFEfHpiPhpRNwaEcsi4paIODki9uyS/3URcX5ELI2IeyPi0oh4a0R0/D0SES+IiNMj4q6IuD8ifhkRH4yItYZaQUmSJEnSyLPBW5Ik9WoBcCZwCLANcBlwKnAXsB9wTkR8rFXGiPgCcAJlAOrzgTOAJwDHAidHxOpt8r0X+CHwHOBy4DRgM+BfgHMjYt1hVU6SJEmSNPps8JYkSb1aDpwC7JGZf56ZL8nMV2fmU4HXAI8AH46IveqZImI/4CDgNmCHKt++wHzgV8C+wNuaNxYRuwBHAPcDu2fmczPzlcBfAD8BngV8YprqKkmSJEkaQTZ4S5KknmTm2Zn5isw8v8W6k4BF1dPXN61+fzU/NDMnanluBw6snr6vRdcm7wMCODIzf1bLdy/wJkoD/EERsdGAVZIkSZIkjRkbvCVJ0rBcUc23aiyIiK2ApwPLgG81Z8jM84BbgC0oV2w38q0JvLB6ekKLfNcDFwNrAi8azu5LkiRJkkadDd6SJGlY5lfzW2vLdqrmV2fmA23yXdKUFuCJwLrAXZn5mz7ySZIkSZLmMBu8JUnSlEXEFsAB1dNTaqu2q+a/7ZD9xqa09cc30l6rfJIkSZKkOWzeTO+AJEkabRExD/gGsCFwVmZ+r7Z6vWp+X4ci7q3m6w8h30omJiY6rR66Vb29qdhlBrY5E6/PXKnnVIza/g7Keo6XVVnP+fPnd08kSZJmBRu8JUnSVH0RWAjcxMoDVkY1zz7LHDTfSlZlI8XExISNIl3MlddnlOo5V45b6zle5ko9JUlS/+zSRJIkDSwijgHeDNwGLMzM25qS3FPN16O9xrp7assGzSdJkiRJmsNs8JYkSQOJiE8Dbwd+T2nsbnVv+eJqvk2HorZuSlt//Ng+80mSJEmS5jAbvCVJUt8i4ijgEOAPwN6ZeU2bpFdU8ydHxDpt0uzalBbgWuABYJOIeFybfM9okU+SJEmSNIfZ4C1JkvoSEUcA7wHupjR2X9kubWbeBFwOrAm8skVZC4CtKF2iXFzLtwz4YfV0/xb5/gLYDVgGnDZoXSRJkiRJ48UGb0mS1LOI+DhwKLCE0tjdy9XVh1fzIyPi8bWyNgOOq54ekZnLm/IdQRm08tCIeEYt33rAVyi/Y47LzCUDVUaSJEmSNHbmzfQOSJKk0RARLwM+VD29Djg4IlolvTYzj2g8ycyTI+J44EDgqog4E3gYWAhsAHwHOLa5kMy8JCLeBxwJXBQRZ1Ma2hcAmwE/Az44pOpJkiRJksaADd6SJKlXm9Qe71JNrZxHuTr7f2XmQRFxAfBWSoP16pR+ur8CHN/i6u5GvqMi4hfAuyl9fa8NXA98DvjXzHxo8OpIkiRJksaNDd6SJKknmbkIWDSF/CcCJw6Q70fAjwbdriRJkiRp7rAPb0mSJEmSJEnSWLDBW5IkSZIkSZI0FmzwliRJkiRJkiSNBRu8JUmSJEmSJEljwQZvSZIkSZIkSdJYsMFbkiRJkiRJkjQWbPCWJEmSJEmSJI0FG7wlSZIkSZIkSWPBBm9JkiRJkiRJ0liwwVuSJEmSJEmSNBbmzfQOSJIkSZIkaW7YcKONBsq3yxS2uXTJkinkljRqvMJbkiRJkiRJkjQWbPCWJEmSJEmSJI0FG7wlSZIkSZIkSWPBBm9JkiRJkiRJ0lhw0EpJkiRpDKzqQcAcAEySJEmz0UBXeEfEOhGxc0Ts1Gb930TE5RHxQETcHBFHRcQ6U9tVSZLUinFZkqTZw7gsSdLMGrRLk/2BS4B/a14REc8Hvg08DVgLeAzwbuDUAbclSZI6My5LkjR7GJclSZpBgzZ4P6+an9Bi3RFAAHcCnwNOq57vHRH7Dbg9SZLUnnFZkqTZw7gsSdIMGrTB+ynV/JL6wojYnnKm+hFgz8x8Z2a+FPgaJYi/ftAdlSRJbRmXJUmaPYzLkiTNoEEHrXx0Nb+paflzqvn5mfmr2vJ/A/4W2HnA7WkMDDqQEjiYkiR1YVyWJGn2MC5LkjSDBr3Ce8Nqfm/T8r8GEjijafn11XyzAbcnSZLaMy5LkjR7GJclSZpBgzZ431PNt2havkc1v6hp+SPV/OEBtydJktozLkuSNHsYlyVJmkGDNnhfW81f2FgQEXsAmwPLgJ81pf/zan7bgNuTJEntGZclSZo9jMuSJM2gQfvw/i6wG/DRiFgG/A44nHJ71mmZ+WBT+kYXzIsH3J4kSWrPuCxJ0uxhXJYkaQYN2uB9LPAW4PHAMdWyAB4CPtoi/T6U4P6TAbcnSZLaMy5LkjR7GJclSZpBA3Vpkpn3U/ofOwG4m9JH2XnAHpl5VT1tRGwFvLh6eubguypJkloxLkuSNHsYlyVJmlmDXuFNZt4GvKGHpHdRzmwD3Djo9iRJUnvGZUmSZo9VFZcjYg1K4/qLgN2BbYBNgd8DFwPHZua5HfK/DjgQ2AFYndL/+Ff5/+zde7RkVX3o++8PkFca6KhpiTRP3WLwBdggHO+AQJODEjAQxBh1GLm5nnN44+PQcEkyvBqkERVRhBwPYo9EW48gylWuPJWXIKd5qAiiG7F5ycMEu+2mwWZ0/+4fa5UURVX13qtqV62q/f2MUWPuWjV/NedsH79dv71qTrggM9d3iXsL8EGK7Vg2B+4Hvgp8MjN/P911SJLUT5UL3lNV/nX7gZkeR5IkbZh5WZKk+uhDXt4fuLr8+THgduApYDfgSODIiPhYZtahR78AACAASURBVP5Ta2BEfB44FngGuBZ4FlhIsSXLwog4KjPXtYk7BTgLWAdcR3EX+/7APwOHRsTCcl2SJA1FpS1N2omITSJiXkTs0K/3lCRJ1ZiXJUmqjxnMy+uBb1Bsl/KnmXloZv5NZr4OeCdFUfofI+KAlvkcSVHsfgx4fRl3BDAB/Aw4Aji+zToWAIuBNcCbM/OgzDwK2IViD/J9gDP6vEZJkqalpzu8I2ILiq8/vZviK1AbURy2sUlTn12Ak4FnMvOUXsaTpEHbZu7cyrELKsatXLGi8pia3czLkiTVxyDycmZ+D/heh9f+V0T8BfD3wHuA7ze9fFrZLsrMyaaYxyPiGIo7t0+NiM+1bG1yKsUBnGdl5q1Ncasj4mhgEjg2Iv6fzPSXWknSUFQueEfEK4BvA7tSJLxOlgOHATtExDeak6IkSeoP87IkSfVRo7x8Z9nOb5rbfOCNwFrg4taAzLw+Ih4BtqO4Y/vmMm5T4K1lt6+0ibs/Im6h2Ev8EGBp/5YhSdLUVdrSJCK2BK4EXk1xGMY/UewP9gLlX4O/RpHk/7raNCVJUifmZUmS6qNmeXmibB9turZH2d6dmU93iFvW0heK4v2WwJOZ+ctpxEmSNFBV7/A+gWKPrgeA/5SZj0bEH3Xp/z1gEcVBFpIkqb/My5Ik1Uct8nJEbAu8r3z6jaaXdi7bbodlPtjSt/nnB+msXZwkSQNV9dDKIyn2Hjs9Mx/dUGfg3rJ9RcXxJElSZ+ZlSZLqY+h5OSI2Ab4MbANcm5nfbnp5Ttk+1eUtVpftVn2IkyRpoKre4f2qsv1+117PWVm2W1ccT5IkdWZeliSpPuqQl/8FWAg8RHFgZbPGnuI5zfesGvcCk5OTG+7UpOph8L2Y7hz7wXXOnGGssxejNt+qXOd4GeQ6JyYmur5eteC9Wdk+M8X+jb/udtofTJIkVWdeliSpPoaalyPiXODvgceAhZn5WEuXVWU7h84ar61qulY17gU2VKiog1GYYz+4zvqZnJwcqflW5TrHS93WWXVLk8fLdpcp9t+rbB+uOJ4kSerMvCxJUn0MLS9HxKeAEykOy1yYme1ut1tetjt2eavtW/o2/7zDNOMkSRqoqgXvm8v2XVPsfyLF155uqDieJEnqzLwsSVJ9DCUvR8QngA8C/wH8RWbe06HrnWX7mojYokOfvVr6QrHX+NPAiyOi037je7eJkyRpoKoWvC+k2L/r+Ij4m06dovBp4M/LS1+oOJ4kSerMvCxJUn0MPC9HxGLgvwO/pSh2/7hT38x8CLgD2BQ4qs177Q/Mp9gS5ZamuLXAd8un724TtwuwL7AWuLzqWiRJ6lWlgndmfg/4GvAiYGlEXAa8v/F6RLw1Iv5v4B7gJIq/Vv+PzPxR71OWJEnNzMuSJNXHoPNyRHwMWASsoCh2T+Xu6jPL9qyIeGXTe80Dzi+fLs7M9S1xi8v5LoqIvZvi5gAXUdQYzs/MFVXWIklSP1Q9tBLgaIoEfiRwaPlonNb8nbJtnOL8NYqvaUmSpJlhXpYkqT4Gkpcj4m3AP5RP7wNOiIh2Xe/NzMWNJ5l5SURcABwD3BUR1wDPAguBrYFvAee1vklmLouIU4GzgJsj4nsUhfb9gXnArcDpVdYiSVK/VC54Z+bvgaMi4q8p/iq9D0VCb1hPkew+nZmX9DRLSZLUlXlZkqT6GGBefnHTzwvKRzvXU9yd3TzHYyPiJuA4ioL1xhT7dF8EXNDm7u5G3Cci4ifAhyj2+t4cuB/4LPDJcu2SJA1NL3d4A5CZlwKXlodd7AJsA6wGlmfm73p9f0mSNHXmZUmS6mOm83JmLgGW9BC/FFhaIe4K4Iqq40qSNJN6Lng3ZObTwN39ej9JklSdeVmSpPowL0uSNDiVDq2UJEmSJEmSJKluKhW8I+JlEfHpiDgrIrq+R0RsHBGLy/5/Um2akiSpE/OyJEn1YV6WJGm4qt7h/TcUB2/M73SQRUNmrgO2K/sfVXE8SZLUmXlZkqT6MC9LkjREVQvef1W2l06x/yVAAIdPd6CI2DUiToqIL0fEvRGxPiIyIt7eJWZJ2afT494usRtFxHERcVtErI6IlRFxY0T87XTnLknSgAwsL0uSpA0yL0uSNERVD63cpWxvm2L/H5XtKyqMdQzFX7ur+AFwX5vrj7brHBEbU/xS8jbgd8BVwGbAQmBpROybmSdWnIskSTNlkHlZkiR1Z16WJGmIqha8ty3bFVPs3+i3bdde7f0UOJvil4XbgS8C+08x9sLMXDKNsU6mKHbfAxyYmY8DRMQEcCNwQkRcm5mXTeM9JUmaaYPMy5IkqTvzsiRJQ1S14P0UsCnwUmDlFPq/tGzXTnegzLyw+XlETPctpqS8u/uU8ukxjWJ3OYfJiFgELAFOByx4S5LqZGB5WZIkbZB5WZKkIaq6h/cvy/agKfb/i7L9VcXxBmFfYB7wcGbe0Ob1i4Fngb0iYruBzkySpO7GMS9LkjSqzMuSJA1R1YL3VRSHapweES/p1jEiXgqcBiRwZcXxqjogIj4dEV+IiI9FxMER0WnNe5TtsnYvZuYa4O7y6e79nqgkST0YlbwsSdJsYF6WJGmIqha8PwesAbYDboqI/dp1Kq/fAGwPPAN8tuJ4Vb0X+ADwfuAfgCuAuyLidW367ly2D3R5vwdb+kqSVAejkpclSZoNzMuSJA1RpT28M/OJiHg/8BXgVcD3I+JBitOlVwFbAW8AdqT4yzbA+zPz0d6nPCU/ojjg8lqKAvbWwJ7AGeW8romIPTPzkaaYOWX7VJf3XV22W3UbfHJyssqcKxv0eFUtGMKYw/i3cZ0zx3XW06jNt6pBrnNiYmJa/UcgL0uSNGuYlyVJGq6qh1aSmV+NiGeALwAvoUjWOzR1aSTu/6BI3t+qPMvpz+0zLZeeAi6PiKuB64F9KL42dnxTn8Z8s9fxp1uo6MXk5ORAxxs1s+XfxnWOl1Fa52z5/6BRWGed87IkSbONeVmSpOGpXPAGyMxvRsSVwHuAhcArKO6mXgXcB1wNLC33vx66zFwbEWcClwGHtLy8qmzn0FnjtVVd+kiSNBSjlpclSRpn5mVJkoajp4I3/OEwxy+Uj1Fwb9lu13J9ednu2CV2+5a+kiTVygjmZUmSxpZ5WZKkwat6aOUoa5ySvbrl+h1lu1e7oIjYEnht+fTOGZiXJEmSJEmSJKkHs7Hg/Y6yXdZy/RbgCWB+h1O0jwJeBCxrOexSkiRJkiRJklQDPW9pEhFzKE6Y3hbYkucO32grM/+11zE3MJ/dgfnAdzNzXdP1TYATywfAOS3zWhcRZwNnAxdExAGZ+UQZOwEsLrueMZPzlySpF3XLy5IkzWbmZUmSBq9ywTsi/pSiOHwksOkUwxKYVgKPiD2B85su7Va2H4+ID//hjTP3KX/cCfgm8GRE/AJ4GNgKeB3wcmA9sCgzr2wz3DnAfsBhwGREXEtxV/dBwObA5zLzsunMX5KkQRhgXt4VeAvFFmALgFdRfHg/KjMv6RCzBPi7Lm/788x8dYfYjYBjgKOBVwPrgJ8A52fmV6czd0mSBmVQeVmSJL1QpYJ3RMwDbgZ2YAN/oW4NrTDc1sCb2lyf6ND/x8C5wN4UB1DuQfGLw8PAl4DPZ+bt7QLLu7wPB46l+GB9MMUH69spPlgvrTB/SZJm1IDz8jHASRXiAH4A3Nfm+qPtOkfExsClwNuA3wFXAZsBC4GlEbFvZp7YLlaSpGEZcF6WJEktqt7h/Q8UxeQEPkdRSP55Zj7dr4k1ZOZ1TCPxZ+avgJN7GG89cF75kCRpFAwsLwM/pbhj7TaKPwh/Edh/irEXZuaSaYx1MkWx+x7gwMx8HP6w1diNwAkRca3fvpIk1cwg87IkSWpRteB9KEXy/lhmfqR/05EkSRUMLC9n5oXNzyNm5ma08u7uU8qnxzSK3eUcJiNiEbAEOB2w4C1JqhM/L0uSNEQbVYx7edl+qV8TkSRJlY1jXt4XmAc8nJk3tHn9YuBZYK+I2G6gM5MkqbtxzMuSJI2Mqnd4/5biQ+jv+jgXSZJUzajk5QMi4vXAHOBx4Cbg6nI7sVZ7lO2ydm+UmWsi4m5g9/LxyAzMV5KkKkYlL0uSNJaq3uF9a9m+ul8TkSRJlY1KXn4v8AHg/RT7m14B3BURr2vTd+eyfaDL+z3Y0leSpDoYlbwsSdJYqnqH96co9iX7EPD2/k1HkiRVUPe8/COKAy6vpShgbw3sCZwBvAG4JiL2zMzmu7TnlO1TXd53ddlu1W3wycnJKnOubNDj9WLBEMYcxr+P65wZo/Tf9YZRnHMVrrP/JiYmptO97nlZkqSxVqngnZk3RsSHgU9FxAXAosz061qSJA1B3fNyZn6m5dJTwOURcTVwPbAPcBpwfFOfxmmY2ev40yxS9GRycnKg442i2fLvMxvWOWprnC3/+3Sdw1f3vCxJ0rirVPCOiIvKH5cD/wV4T0T8EPg1sK5LaGbm31cZU5IktTeqeTkz10bEmcBlwCEtL68q2zl01nhtVZc+kiQN1KjmZUmSxkXVLU3ex3N3XAXwR8BCut+FFeXrJnBJkvrrfYxuXr63bLdrub68bHfsErt9S19JkurgfYxuXpYkaeRVLXjfQB++YixJkvpilPPyS8p2dcv1O8p2r3ZBEbEl8Nry6Z0zMC9Jkqoa5bwsSdLIq7qH95/3eR6SJKmiEc/L7yjbZS3XbwGeAOZHxH6ZeUPL60cBLwKWtRx2KUnSUI14XpYkaeRtNOwJSJKk8RURu0fEoRGxccv1TSLig8CJ5aVzml/PzHXA2eXTCyJiXlPsBLC4fHrGzMxckiRJkjSKqm5pIkmSZqGI2BM4v+nSbmX78Yj4cONiZu5T/rgT8E3gyYj4BfAwsBXwOuDlwHpgUWZe2Wa4c4D9gMOAyYi4luKu7oOAzYHPZeZlfVqaJEmSJGkM9KXgHRGvAxYAfwJsnpkf7cf7SpKk6ZvhvLw18KY21yc69P8xcC6wN8UBlHtQ7Gv6MPAl4POZeXu7wMxcFxGHA8cCRwMHA+uA24HzM3NpD+uQJGkg/LwsSdJg9VTwjoiDgE/x3KFRDR9t6vMqin05fw/snJlP9TKmJElqbxB5OTOvA2Ia/X8FnDydMVri1wPnlQ9JkkaGn5clSRqOynt4R8T/BVxB8ZXkAP6dNh+AM/MXwG3AS4C/rDqeJEnqzLwsSVJ9mJclSRqeSgXviPgz4IIy/t+AHYBXdAm5hCK5/1WV8SRJUmfmZUmS6sO8LEnScFXd0uRDwMbAtzLz7wAi4o+69P/fZfvGiuNJkqTOzMuSJNWHeVmSpCGquqXJARQHTp09xf4Ple3LK44nSZI6My9LklQf5mVJkoaoasG7kYh/NsX+a8t2s4rjSZKkzszLkiTVh3lZkqQhqlrwfqZst5hi/0bCX1FxPEmS1Jl5WZKk+jAvS5I0RFX38F4OvB5YAHx7Cv0PLtt7Ko4nSZI6W455ua+2mTu3UtyCHsZcucI6hySNieWYlyVJGpqqd3hfSXGK9Ic31DEi5gH/nWIPs+9WHE+SJHVmXpYkqT7My5IkDVHVgve5wNPA/xER34mIl7brFBFvBq4HtqX4etb/qDieJEnqzLwsSVJ9mJclSRqiSgXvzHwU+Pvy6VuBRykSNQAR8b8i4hfADcCuwHrg7zJzZW/TlSRJrczLkiTVh3lZkqThqnqHN5n5NeCvgH8HNgb2bHr57cArKb7G9QRwWGZ+p4d5SpKkLszLkiTVh3lZkqThqXpoJQCZ+Z2I2AH4W+Agir9ObwOsBu4HrgK+nJlrep2oJEnqzrwsSVJ9mJclSRqOngreAJn5e2BJ+ZAkSUNkXpYkqT7My5IkDV6lgndEfLr88euZ+cM+zkeSJE2TeVmSpPowL0uSNFxV7/A+qWw9RVqSpOEzL0uSVB/mZUmShqjqoZW/Kdsn+jURSZJUmXlZkqT6MC9LkjREVQvePy3bXfo1EUmSVJl5WZKk+hhoXo6IXSPipIj4ckTcGxHrIyIj4u1dYpaUfTo97u0Su1FEHBcRt0XE6ohYGRE3RsTfzswKJUmanqpbmlwEHAj8N+D9/ZuOJEmqwLwsSVJ9DDovH8Nz26hM1w+A+9pcf7Rd54jYGLgUeBvwO+AqYDNgIbA0IvbNzBMrzkWSpL6oVPDOzKUR8ZfA/xkRvwE+kplr+zs1SZI0FeZlSZLqYwh5+afA2cBtwO3AF4H9pxh7YWYumcZYJ1MUu+8BDszMxwEiYgK4ETghIq7NzMum8Z6SJPVVpYJ3RPwT8Avg18Ai4L9ExPeA+4E13WIz86NVxpQkSe2ZlyVJqo9B5+XMvLBl/Om+xZSUd3efUj49plHsLucwGRGLgCXA6YAFb0nS0FTd0uQjQJY/B/Bi4MgpxvrBWpKk/voI5mVJkuriI4xnXt4XmAc8nJk3tHn9YuB/AntFxHaZ+chAZydJUqlqwftBnkvgkiRpuMzLkiTVxyjl5QMi4vXAHOBx4Cbg6sxc36bvHmW7rN0bZeaaiLgb2L18WPCWJA1F1T28d+rzPCRJUkXmZUmS6mPE8vJ721y7JyLemZl3tVzfuWwf6PJ+D1IUu3fu0keSpBm10bAnIEmSJEmSBupHwInAayju7n45cCjwY2A34JqI2K4lZk7ZPtXlfVeX7Vb9m6okSdNTdUsTSZIkSZI0gjLzMy2XngIuj4irgeuBfYDTgOOb+jROw+x5u5bJyclp9V/Q64AVTHeO/eA6Z84w1tmLUZtvVa5zvAxynRMTE11ft+AtSZIkSZLIzLURcSZwGXBIy8urynYOnTVeW9WlzwYLFXUwCnPsB9dZP5OTkyM136pc53ip2zorFbwjot0+X1OSmf9aNVaSJL2QeVmSpPoYg7x8b9m2bmmyvGx37BK7fUtfSZIGruod3kuo9jWmBOqQwCVJGidLMC9LklQXSxjtvPySsl3dcv2Ost2rXVBEbAm8tnx65wzMS5KkKenl0Mqo8PCQTEmSZoZ5WZKk+hjlvPyOsl3Wcv0W4AlgfkTs1ybuKOBFwLLMfGQG5ydJUleVEmpmbtTtQZHkdgT+G/AIcB+wW/maJEnqI/OyJEn1Ufe8HBG7R8ShEbFxy/VNIuKDwInlpXOaX8/MdcDZ5dMLImJeU+wEsLh8esbMzFySpKmZkYSamesy86HM/ALFAbybAFdGxB/PxHiSJKkz87IkSfXR77wcEXtGxA8bD2DP8qWPt1xv2An4NvBERNwSERdHxBXAA8Cnyj6LMvPKNsOdU8buBkxGxKUR8W3gJ8C2wOcy87Iq65AkqV9m/C/Imfk48E8Uh1ecOtPjSZKkzszLkiTVR5/y8tbAm5oeW5XXJ1quN/wYOBf4ObADcBiwP7AG+BKwd2Z+osN81wGHAydQ3Jl+cBl7O/DuzDyxXZwkSYNU9dDK6fpe2R4BLBrQmJIkqT3zsiRJ9dFTXs7M6yj2AJ9q/18BJ093nKb49cB55UOSpNoZ1N6dz5Tt/AGNJ0mSOjMvS5JUH+ZlSZL6aFAF7zeX7VMDGk+SJHVmXpYkqT7My5Ik9dGMF7wj4nXAZ4EEbp3p8SRJUmfmZUmS6sO8LElS/1XawzsiLppCty2AXYE3UOwntg5YXGU8SZLUmXlZkqT6MC9LkjRcVQ+tfB/FX6A3pHFwxirgmMy8qeJ4kiSps/dhXpYkqS7eh3lZkqShqVrwvoHuCTwpDt54lOJrWRdn5m8rjiVJkrozL0uSVB/mZUmShqhSwTsz/7zP85AkSRWZlyVJqg/zsiRJwzXjh1ZKkiRJkiRJkjQIFrwlSZIkSZIkSWOh0pYmEbEF8BcUe49dnpnru/TdGDiE4kCOKzPz91XGlCRJ7ZmXJUmqD/OyJEnDVfUO78OBbwIf7Ja8ATJzHXBy2f+wiuNJkqTOzMuSJNWHeVmSpCGqWvB+e9l+ZYr9v0LxF+t3VBxPkiR1Zl6WJKk+zMuSJA1R1YL3a8r2B1Psf3PZvrbieJIkqTPzsiRJ9WFeliRpiKoWvOeX7aNT7P9Y2W5XcTxJktSZeVmSpPowL0uSNERVC97rynbLKfZv9Nu44niSJKkz87IkSfVhXpYkaYiqFrwfKdu9p9j/TWX764rjSZKkzszLkiTVh3lZkqQh2qRi3HXAq4FTIuL/7XbydERsBHwYSOD6iuNJkqTOrsO8LGkW2Gbu3MqxCyrGrVyxovKYmrWuw7wsSdLQVL3D+18oEvKbgK9GxFbtOkXEHIoTp/ctL11QcTxJktSZeVmSpPowL0uSNESV7vDOzJ9ExDnAB4G3A/85Ir4F/AhYBWwF7A4cDmxdhp2bmXf0PmVJktTMvCxJUn2YlyVJGq6qW5oAnFLGnwhsA7y3fDSLsj2H4mta0xYRuwJvAfai+Cbiq8r3PSozL9lA7LuAY4DXUxwAci/wJeCCDXyt7C0Uv5wsADYH7ge+CnwyM39fZR2SJM2wgeRlSZI0JeZlSZKGpOqWJmTm+sw8meLrV18DfkORsBuP3wBLgX0y80OZmRWHOgb4DPBuYFee+6Wgq4j4PMXXwxYANwJXUxTLzwMuiYi2J2BHxCnAd4EDgTuAy4F5wD8D10XEVE/aliRpYAaYlyVJ0gaYlyVJGp5e7vAGIDNvBd4Ff9iDbGtgVWau6vW9Sz8FzgZuA24Hvgjs3y0gIo4EjgUeA/bLzMny+suA7wNHAMcD57bELQAWA2uAA8u1NdZ1ObAfcAbwgT6tTZKkvhpAXpYkSVNkXpYkafAq3+HdTmauzsxf9zN5Z+aFmXlKZn49M385xbDTynZRo9hdvtfjFHeMA5xanojd7FSKv7af1Sh2l3GrgaOB9cCxEVH9eHhJkgZkJvKyJEmqxrwsSdJg9LXgXQcRMR94I7AWuLj19cy8HngE2BbYpyluU+Ct5dOvtIm7H7gF2BQ4pO8TlyRJkiRJkiT1pFLBOyJ2johLI+Lf2twl3dp344j4ckR8IyK2rzbNadmjbO/OzKc79FnW0heK/cG3BJ7scid5uzhJkoaq5nlZkqRZxbwsSdJwVb3D+53A4cCazFzfrWNmrgNWlf3fWXG86di5bB/o0ufBlr7NPz9IZ+3iJEkatjrnZUmSZhvzsiRJQ1S14H0IkMBlU+x/GcXe2IdWHG865pTtU136rC7brfoQJ0nSsNU5L0uSNNuYlyVJGqJNKsbtVLY/nmL/u8p2x4rjTUeUbQ4o7gUmJyc33KmPBj1eVQuGMOYw/m1c58xxnfU0avOtapDrnJiYmG7ITmVbx7wsSdJss1PZmpclSRqCqgXvPynb1V17PafR72UVx5uOxonXc7r0abzWfDp21bgXqFCoqGxycnKg442a2fJv4zrHyyitc7b8f9AIrLPOeVmSpNnGvCxJ0hBV3dJkZdm+fIr9/7Rsu20X0i/Ly7bbX8cbh4Esb7rW+HmHacZJkjRsA8vLEbFrRJxUHrB1b0Ssj4iMiLdPIfZdEXFjRKyMiNURcVtEHDeFA73eEhFXRcSTEbEmIn4aEadHxGbTnb8kSQNQ58/LkiSNvaoF73vLdqp7jB1WtoP4PvidZfuaiNiiQ5+9WvpCsaangRdHxCs6xO3dJk6SpGEbZF4+BvgM8G5gV57bEqyriPg88BWKnYJuBK4GXgWcB1wSERt3iDsF+C5wIHAHcDkwD/hn4LqI2LLCGiRJmkl1/rwsSdLYq1rw/v8oPuAuiohdunUsX19EsTf2dyqON2WZ+RDFB+JNgaPazGd/YD7wGHBLU9xaig/UUHyIb43bBdgXWEvxYVuSpLoYZF7+KXA28DfAK4HrNxQQEUcCx1Lk3tdn5qGZeQQwAfwMOAI4vk3cAmAxsAZ4c2YelJlHAbsANwD7AGdUWIMkSTOptp+XJUmaDaoWvC8A/h34Y+CWiHhvRGza3CEiNo2I9wI3Ay8GfktxF9cgnFm2Z0XEK5vmNA84v3y6ODPXt8QtpvhFY1FE7N0UNwe4iOLf6/zMXDFjM5ckafoGlpcz88LMPCUzv56Zv5xi2Glluygz/3D3WmY+TnHHOMCpbbY2OZWiYHBWZt7aFLcaOBpYDxwbEXOnuw5JkmZQ3T8vS5I01ioVvDPzd8A7gWeBlwJfAlZExJ0RcUNE3AmsKK/Po7gr+h2ZubLTe3YSEXtGxA8bD2DP8qWPt1xvnt8lFL9kbAvcFRHfjohLKb4ithvwLdr8MpGZyyg+XG8J3FzuF/p14JfA/sCtwOnTXYMkSTNpkHl5uiJiPvDGcsyL28z9euARipy9T1PcpsBby6dfaRN3P8U3tTYFDun7xCVJqqjOeVmSpNlgk6qBmfm9iNgPWAK8GtgceEObrvcAR5fF5Cq2Bt7U5vrEBuZ3bETcBBxHUazemGIvtYuAC9rc3d2I+0RE/AT4EMVe35sD9wOfBT6Zmb+vuA5JkmbMAPPydO1Rtndn5tMd+iwDtiv73lxe25XiD9BPdrmTfBnw5jJuaX+mK0lS72qclyVJGnuVC94Amfm/gd0i4j8DC4FXUBSoVwH3AVdn5jU9jnEdUzwQq03sUip8AM7MK4ArqowpSdKwDCIvV7Bz2T7Qpc+DLX2bf36QztrFSZJUCzXNy5Ikjb2eCt4NmXkVcFU/3kuSJPWmZnl5Ttk+1aXP6rLdqg9xLzA5Odnt5bYWTDuid1Xm2SvXOXNmwzpnwxphOOvs1SjOuYpBrnNiousXjLuqWV6WJGns9VTwjojNKL6C/OLy0m+Bh932Q5KkwatpXm58SysHFPcCvRQpBmlU5tkr1zk+ZsMaYfTWOTk5OXJzrmIU1lnTvCxJ0tibdsE7IrYG/itwBMUBki9q6fJseQjHN4D/6cEbkiTNnBHIy6vKdk6XPo3XVjVdqxonSdLQjEBeliRp7E2r4B0RRwOf4bkPmO321t4U2Lt8/GNEnJSZS3qZpCRJeqERycvLy3bHLn22b+nb/PMO04yTJGkoRiQvSxqQbebOrRTXlmO6kwAAIABJREFUy/ZdK1es6CFaGh9TLnhHxGeAE3guaa8Bbqc4Vbrxv6i5wJ8BbwT+iGJPzS9GxBsy8wP9mrQkSbPdCOXlO8v2NRGxRWY+3abPXi19Ae4FngZeHBGvyMxftonbu02cJEkDN0J5WZKksTelgndEnAScWD59DPhH4KuZuaZD/y2BdwIfBV4OnBgRyzPz3N6nLEnS7DZKeTkzH4qIOyi+1n0U8K8tc9sfmE+xjlua4tZGxHeBvwbeXc69OW4XYF9gLXD5TK5BkqRuRikvS5I0G2y0oQ4R8TLgYxSHRv0A+LPM/GKn5A2QmWsy8yJgN+Amir9yfzQi5vVn2pIkzU4jmpfPLNuzIuKVjYvl+OeXTxdn5vqWuMUU61wUEXs3xc0BLqL4Peb8zPS7m5KkoRjRvCxJ0ljbYMEbOJpiD7JHgb+czqEamfk74FDg1+V7HF1lkpIk6Q+GmpcjYs+I+GHjQXHnNsDHW643j3sJcAGwLXBXRHw7Ii4FJik+7H8LOK/NfJcBpwJbAjdHxFUR8XXgl8D+wK3A6dNdgyRJfeTnZUmSamYqBe+3Uvy1+pNlQp6WMuaTFH+1PmS68ZIk6XmGnZe3Bt7U9NiqvD7Rcr113GMptia5g6JYfTBwH3A8cGRmrusw309QrPn7FHt9Hwb8O/APwP7d7qCTJGkAhp2XJUlSi6ns4d346vGVPYzTiH1l116SJGlDhpqXM/M6njuQa7qxS4GlFeKuAK6oMqYkSTPMz8uSJNXMVO7wfknZPtbDOI3Yl3TtJUmSNsS8LElSfZiXJUmqmakUvBtfy5rbwziN2Gl/xUuSJD2PeVmSpPowL0uSVDNTKXg/VLZv7mGcRuxDXXtJkqQNMS9LklQf5mVJkmpmKgXvayj26jwxIqa9Z2dEbAScRHGQx7XTjZckSc9jXpYkqT7My5Ik1cxUCt5fBtYDbwTOqTDGJ8vYBP6tQrwkSXqOeVmSpPowL0uSVDMbLHhn5l3Alyj+an1CRHw7InbZUFxE7BwRl/HcX6uXlO8lSZIqMi9LklQfw87LEbFrRJwUEV+OiHsjYn1EZES8fQqx74qIGyNiZUSsjojbIuK48q7zbnFviYirIuLJiFgTET+NiNMjYrPpzl+SpJmwyRT7nQD8GfCfgEOAt0bEDcD1wD3ACook/cdlv/3LR5SPW4Dj+zpzSZJmL/OyJEn1Mcy8fAxF0XxaIuLzwLHAMxRbqTwLLATOAxZGxFGZua5N3CnAWcA64DrgtxRr+Wfg0IhYmJlrqi1FkqT+mFLBOzOfiYi3AP8CvIsiKTeSdCeN/cu+BvzXzHyml4lKkqSCeVmSpPoYcl7+KXA2cBtwO/DFDYxLRBxJUex+DNgvMyfL6y8Dvg8cQVGAP7clbgGwGFgDHJiZt5bX5wCXA/sBZwAfqLgWSZL6Yip7eAOQmasz8z3AwcAVFPuURYfHeuAq4C2Z+a7MXNXviUuSNJuZlyVJqo9h5eXMvDAzT8nMr2fmL6cYdlrZLmoUu8v3epzijnGAU9tsbXJqOf+zGsXuMm41cDTFuo6NiLlV1iJJUr9MdUuTP8jMq4Gry7/i7gPsTPHVrACeBJYDt5RJT5IkzSDzsiRJ9VH3vBwR8ykOyVwLXNz6emZeHxGPANtRzP/mMm5T4K1lt6+0ibs/Im4B3kyxrcvSGVmAJElTMO2Cd0OZoK/p41wkSVJF5mVJkuqjxnl5j7K9OzOf7tBnGUXBew/KgjewK7Al8GSXO8mXURS898CCtyRpiKa8pYkkSZIkSRppO5ftA136PNjSt/nnB+msXZwkSQNX+Q5vSdL42GZuta0WF/Qw5soVK3qIliRJUgVzyvapLn0a261s1Yc4SZIGzoK3JEmSJEmzQ5RtDiiurcnJyQ13atLLTRZVTXeO/eA6Z47rrKdRm29VrrP/JiYmur5uwVuSJEmSpNlhVdnO6dKn8dqqpmtV49raUKGiDkZhjv3gOsfLKK1zcnJypOZblescDvfwliRJkiRpdlhetjt26bN9S9/mn3eYZpwkSQNnwVuSJEmSpNnhzrJ9TURs0aHPXi19Ae4FngZeHBGv6BC3d5s4SZIGzoK3JEmSJEmzQGY+BNwBbAoc1fp6ROwPzAceA25pilsLfLd8+u42cbsA+wJrgcv7PnFJkqbBgrckSZIkSbPHmWV7VkS8snExIuYB55dPF2fm+pa4xRSHVi6KiL2b4uYAF1HUF87PzBUzNnNJkqbAQyslSZIkSRpBEbEnzxWpAXYr249HxIcbFzNzn6afL4mIC4BjgLsi4hrgWWAhsDXwLeC81rEyc1lEnAqcBdwcEd8DVgD7A/OAW4HT+7g8SZIqseAtSZIkSdJo2hp4U5vrE92CMvPYiLgJOI6iYL0xxT7dFwEXtLm7uxH3iYj4CfAhir2+NwfuBz4LfDIzf191IZIk9YsFb0mSJEmSRlBmXgdExdilwNIKcVcAV1QZU5KkQXAPb0mSJEmSJEnSWLDgLUmSJEmSJEkaC25pUgPbzJ1bOXZBxbiVKzw4W5IkSZIkSdJ48Q5vSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBW5IkSZIkSZI0Fix4S5IkSZIkSZLGggVvSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBW5IkSZIkSZI0Fix4S5IkSZIkSZLGggVvSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBW5IkSZIkSZI0Fix4S5IkSZIkSZLGggVvSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBW5IkSZIkSZI0Fix4S5IkSZIkSZLGwtgWvCNiSURkl8e9HeI2iojjIuK2iFgdESsj4saI+NtBr0GSJEmSJEmSNHWbDHsCA/AD4L421x9tvRARGwOXAm8DfgdcBWwGLASWRsS+mXniDM5VkiRJkiRJklTRbCh4X5iZS6bY92SKYvc9wIGZ+ThAREwANwInRMS1mXnZjMxUkiRJkiRJklTZ2G5pMl3l3d2nlE+PaRS7ATJzElhUPj190HOTJEmSJEmSJG2YBe/n7AvMAx7OzBvavH4x8CywV0RsN9CZSZIkSZIkSZI2aDYUvA+IiE9HxBci4mMRcXBEtFv3HmW7rN2bZOYa4O7y6e4zMVFJksaZB0pLkiRJkmbabNjD+71trt0TEe/MzLuaru1ctg90ea8HKYrdO3fpI0mSuvNAaUmSJEnSjBjngvePgNuBaymK2FsDewJnAG8AromIPTPzkbL/nLJ9qst7ri7brboNPDk5Oa2JLphW7/6Y7hz7wXXOHNc5c1znzBnGOnsxyPlOTEwMbKwh8UBpSZIkSdKMGNuCd2Z+puXSU8DlEXE1cD2wD3AacHz5ejRCex17FAoVozDHfnCd48V1jpdRWufk5ORIzXdcbOhA6YhYBCyhOFDagrckSZIkaVbs4f08mbkWOLN8ekjTS6vKdg6dNV5b1aWPJEnqDw+UliRJkiRNy9je4b0BjUOxmj8cLy/bHbvEbd/SV5IkTd8BEfF6ij8kPw7cBFydmetb+m3wQOmIuJvifI3dgUfa9ZMkSZIkzR6zteD9krJd3XTtjrLdq11ARGwJvLZ8eucMzUuSpNnAA6UlSZIkSTNitha831G2zXeM3QI8AcyPiP3afHX6KOBFwLKmgy4lSdLUDeVA6SoHjs6Wg1xd58yZDeucDWuE0TtkGUZzzlV4oLQkSWpnLAveEbE7MB/4bmaua7q+CXBi+QA4p/FaZq6LiLOBs4ELIuKAzHyijJsAFpddzxjAEiRJGjvDOlB6VIoUozLPXrnO8TEb1gijt87ZctDybFmnJEmavrEseAM7Ad8EnoyIXwAPU9z59Trg5cB6YFFmXtkSdw6wH3AYMBkR11Lc1X0QsDnwucy8bCArkCRplsjMtRFxJnAZHigtSZIkSerBuBa8fwycC+xNcQjlHhR3hz0MfAn4fGbe3hpU3uV9OHAscDRwMLCO4uvX52fm0sFMX5KkWccDpSVJkiRJPRvLgndm/go4uWLseuC88iFJkgbDA6UlSRqgiFgC/F2XLj/PzFe3idsIOIbiJrFXU9wk9hOKm8S+OgNTlSRpWsay4C1JkkaOB0pLkjQcPwDua3P90dYLEbExcCnwNuB3wFXAZsBCYGlE7JuZJ7bGSZI0SBa8JUnSjPNAaUmSauvCzFwyxb4nUxS77wEOzMzH4Q95+UbghIi41rOvpNljm7lzK8Ut6GHMlStW9BCt2cCCtyRJGoSd8EBpSZJGVnl39ynl02MaxW6AzJyMiEXAEuB0ioOoJUkaio2GPQFJkjQrNA6U/jmwA0UBe39gDcWB0ntn5idag8q7wQ8HTqD4uvXBZdztwLv92rQkSQOzLzAPeLjNNmMAFwPPAntFxHZtXpckaSC8w1uSJM04D5SWJKm2DoiI1wNzgMeBm4Cry/zbbI+yXUYbmbkmIu4Gdi8fnq8hSRoKC96SJEmSJM1e721z7Z6IeGdm3tV0beeyfaDLez1IUezeuUsfSZJmlAVvSZIkSZJmnx9RbBF2LUURe2tgT4rDoN8AXBMRe2Zm407tOWX7VJf3XF22W3UbeHJycloT7eVwu6qmO8d+cJ0zx3XOnNmyzl6M2nyrGuQ6JyYmur5uwVuSJEmSpFkmMz/Tcukp4PKIuBq4HtgHOA04vnw9GqG9jr2hQkUdjMIc+8F1jhfXWT+Tk5MjNd+q6rZOD62UJEmSJEkAZOZa4Mzy6SFNL60q2zl01nhtVZc+kiTNKAvekiRJkiSp2b1lu13TteVlu2OXuO1b+kqSNHAWvCVJkiRJUrOXlO3qpmt3lO1e7QIiYkvgteXTO2doXpIkbZAFb0mSJEmS1OwdZbus6dotwBPA/IjYr03MUcCLgGVNB11KkjRwFrwlSZIkSZpFImL3iDg0IjZuub5JRHwQOLG8dE7jtcxcB5xdPr0gIuY1xU0Ai8unZ8zczCVJ2rBNhj0BSZIkSZI0UDsB3wSejIhfAA8DWwGvA14OrAcWZeaVLXHnAPsBhwGTEXEtxV3dBwGbA5/LzMsGsgJJkjqw4C1JkiRJNbLN3LmVYxdUjFu5YkXlMTWSfgycC+xNcQjlHkBSFL6/BHw+M29vDcrMdRFxOHAscDRwMLAOuB04PzOXDmb6kiR1ZsFbkiRJkqRZJDN/BZxcMXY9cF75kCSpdtzDW5IkSZIkSZI0Fix4S5IkSZIkSZLGggVvSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBW5IkSZIkSZI0Fix4S5IkSZIkSZLGggVvSZIkSZIkSdJYsOAtSZIkSZIkSRoLFrwlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjYVNhj0BSZIGZZu5cyvFLehhzJUrVvQQLUmSJEmSpsM7vCVJkiRJkiRJY8GCtyRJkiRJkiRpLFjwliRJkiRJkiSNBQvekiRJkiRJkqSxYMFbkiRJkiRJkjQWLHhLkiRJkiRJksaCBW9JkiRJkiRJ0liw4C1JkiRJkiRJGgsWvCVJkiRJkiRJY8GCtyRJkiRJkiRpLFjwliRJkiRJkiSNBQvekiRJkiRJkqSxYMFbkiRJkiRJkjQWLHhLkiRJkiRJksaCBW9JkiRJkiRJ0liw4C1JkiRJkiRJGgsWvCVJkiRJkiRJY8GCtyRJkiRJkiRpLFjwliRJkiRJkiSNBQvekiRJkiRJkqSxYMFbkiRJkiRJkjQWLHhLkiRJkiRJksaCBW9JkiRJkiRJ0ljYZNgTkCRJkiRJkqS62mbu3EpxC3oYc+WKFT1Ez27e4S1JkiRJkiRJGgsWvCVJkiRJkiRJY8GCtyRJkiRJkiRpLFjwliRJkiRJkiSNBQvekiRJkiRJkqSxYMFbkiRJkiRJkjQWNhn2BCRJkiRJs882c+dWjl1QMW7lihWVx5QkSaPBO7wlSZIkSZIkSWPBgrckSZIkSZIkaSxY8JYkSZIkSZIkjQUL3pIkSZIkSZKksWDBu4OIeFdE3BgRKyNidUTcFhHHRYT/ZpIkDZh5WZKkejE3S5LqykTURkR8HvgKxeHfNwJXA68CzgMuiYiNhzg9SZJmFfOyJEn1Ym6WJNWZBe8WEXEkcCzwGPD6zDw0M48AJoCfAUcAxw9xipIkzRrmZUmS6sXcLEmqu02GPYEaOq1sF2XmZONiZj4eEccA1wGnRsTnMnP9MCYoSdIsYl6WJKlezM2SNKa2mTu3UtyCHsZcuWJFD9HteYd3k4iYD7wRWAtc3Pp6Zl4PPAJsC+wz2NlJkjS7mJclSaoXc7MkaRRY8H6+Pcr27sx8ukOfZS19JUnSzDAvS5JUL+ZmSVLtuaXJ8+1ctg906fNgS9+ezcSt+3XkOseL6xwvrlM1NZS8DLPnvyuuc7zMhnXOhjWC61St+Zl5BrnO8eI6x4vrHC3e4f18c8r2qS59VpftVjM8F0mSZjvzsiRJ9WJuliTVngXv54uyzaHOQpIkgXlZkqS6MTdLkmrPLU2eb1XZzunSp/HaquaL22yzTbTpK0mSqjMvS5JUL+ZmSVLteYf38y0v2x279Nm+pa8kSZoZy8vWvCxJUj0sL1tzsySptix4P9+dZfuaiNiiQ5+9WvpKkqSZYV6WJKlezM2SpNqz4N0kMx8C7gA2BY5qfT0i9gfmA48Btwx2ds+bx7si4saIWBkRqyPitog4LiLG4j/PiNg1Ik6KiC9HxL0RsT4iMiLePuy59UtEvCgiFkbEpyLihxHxaESsjYhHIuKSiPjzYc+xXyLihIj4ekT8LCL+IyKejYjfRMQ1EfGeiBjbrzZGxMfL/+5mRHx42PPph4hY0rSmdo97hz3HfoqILeL/b+/OoyUp6zOOfx9mYNgkwLDJIoMjyKIgKA4BlU0Sj0EkzmA8IcJAUBR3FBA1OIFE0LhGIBpFJwYxQlgEMRHBDIEQEVSIgMjmoCzD6sg+M8Avf7xvc2ua3u693be6qp/POe+p7q63qn/VVd1P365bVdKxkq6RtFTSE5J+I+kcSXuUXV/dVSWXcy3O5opzNtc/m+uYyzBa2excLl9Vstm5XH3OZedyVY1SLsPwZrPP4f18JwPnAJ+WdFVE3AYgaSPg9NznlIh4toziJJ0GHAU8BVwGrAD2BU4F9pV0UEQ8U0ZtffRu4ANlFzFgewI/yreXAD8jXel8e2AuMFfSSRFxQkn19dNxwEbADcBVpOXcEtiHtO3Ok/SWst5TgyJpV+BY0gV96vgF5X+A21o8fu9UFzIokrYCLgFeAtwPXA4sA2YBbwauJ70ONlhDncu5FmdzPTiba5zNI5DLUPNsdi4PlaHOZudybTiXnctVV+tchiHP5ohwa2qkkA7gSeAi4DzgD/mx84FpJdU1N9dwL7B14fGNgZvyuA+U/fr1YTmPAD4DvBWYDSzKyzav7Nr6uIz7AP8OvLbFuL8Ans7LvHfZtfZhWV8DrNXi8R1IX1wCOKzsOvu8zDOAG4G782dGAB8pu64+LdvCvDzzy65lwMu5FunLSQAnAqs2jZ8JbFN2naPShjWXc23O5iGor0/L6GyuaTbXOZfz8tU+m53Lw9eGNZudy87lKjbnsnO5im3Ys7kWh/P0W0QcBRxMOlRrT+BPSSvxvcDcKG9v8PF5eFxE3Np4MCLuI+3hBfho1Q/TioivR8SxEXF2RNxedj2DEBE/joh5EXFFi3HfJX1AAvzVlBY2ABFxZUQ83uLxG4HT8t39praqgTuR9J8H7yJ98bfq+QTpj4dvRcQJEbGiODIiHoqIW8opbfQMcS6Ds7k2nM21zmbncvU5l4fMEGezc7kmnMvOZRt6Q53NPqVJGxFxFnBW2XU0SNoceCWwnHT42Eoi4nJJdwObAbuRDoOx6mpc4GXzUqsYvKfz8KlSq+gjSXOADwNnRcRFkuaWXZONj6TVgHfku6eUWYuNGbZcBmfzCHI2V5Bzufqcy8Nr2LLZuTxynMsV5Fyuhypks3/wro6d8/DGiHiyTZ9rSOG9Mw7vqts6D2tzbqdm+VxP78p3Lyqzln6RtDrwL8DD1P+centL2hFYG7gPuBL4UdTjvHKvJB1+9buI+JWk3YH982NLgP+MiFIvkGhDw9k8WpzNFTNiuQz1zWbnsvXKuTxanMsV41yuTS5DBbLZP3hXx1Z5eGeHPr9t6msVJGkTYH6+e26JpfSVpMNIhzuuStoLvzuwCnByRJxfZm199PfAS4G3RcSDZRczYIe0eOwmSW+LiF9OeTX99fI8vFXSQuDQpvEnSDoXeHuHP6ZsNDibR4SzubJGKZehvtnsXLZeOZdHhHO5spzL9chlqEA2+wfv6lg7D593XqeCx/LwBQOuxQZE0nTgTOCPgMsiovJ7cQv2YOUPwaeBvwE+X045/ZX3aH4QuCCfU66uriNdIf0y0h8T6wC7kL687ARcKmmXiLi7vBInbf08fB0wDfgs8BXgofzY6aQLIj0CHF5GgTY0nM0jwNlcTSOUy1D/bHYuW6+cyyPAuVxNzuVa5TJUIJsrfaGGEaM8jFKrsEH7CrAv8DtqcPGNoog4IiIErEm62vQXgQXATyRtWmZtkyVpDeCbpA/zo0ouZ6Ai4osR8eWIuCkiHo+IeyPiYuDVwE+AjRi7WFBVNbJxOnBGRBwTEbdHxNKIuBA4kPRZfKikF5dWpQ0DZ/NocDZXzCjlMoxENjuXrVfO5dHgXK4Y53LtchkqkM3+wbs6Hs3DtTv0aYx7tEMfG1KSvgT8Nel8R/tGxJKSSxqIiHgyf/AfQ/qQ3wk4teSyJutTwDbA0RFR23PIdRIRy4GT8903lllLHxQ/Q7/WPDIiriXtsV8F2GuKarLh5GyuOWdzZY18LkOtstm5bL1yLtecc7mynMvUKpehAtnsH7yrY3EebtmhzxZNfa0iJH0OeD/wACm4by25pKnyzTx8k6RVS61kcv4ceJa093JRsQFvyH3enR/7emlVDt7NebhZqVVM3uLC7d+06dN4fJPBlmJDbnEeOptryNlc6Wx2Lo+pQzYvLtx2Llsni/PQuVxDzmXnck3UIZehAtnsc3hXxy/ycAdJa7Q56fuuTX2tAiR9BjiadK6j/SLippJLmkpLSeclm046B9R95ZYzKauQLjDSzotzW3dqyinFzDx8rGOv4ffzwu2ZpC/VzTbIw6ovq02Os7mmnM21yGbnclKHbHYuW6+cyzXlXHYu10gdchkqkM3+D++KiIjfkTao1YCDmsdL2pN0Fd8lwP9ObXU2UZJOAY4Bfk8K7utLLmmqvY4U3EuByl6lOSJmRYRaNeBfcrdj8mOvKLPWAXtrHl5TahWTlC8ecnW+u2/zeEnrkS46AnDtVNVlw8fZXE/O5upns3N5JZXPZuey9cq5XE/OZedyzVQ+l6Ea2ewfvKulca6fT0t6SeNBSRuRroAKcEpEPDvlldm4SToJOI4UXPtFRO3+y0DSayUdLGlGi3F7AGfku2dExDNTW52Nl6RXSNpf0rSmx6dLOpp0iCHAF6a+ur77+zw8QdJzX7okrQ78E+mq8D/DfyyZs7lWnM3O5qoZoWx2LluvnMs14lx2LlfNCOUyDHk2K8IXMK4SSacD7waeAi4FVpD2pqwDXADMq/qHoKRdGPsyArA98ALgVuDhxoMRsdsUl9Y3kg4AvpfvXgvc2KbrzRFxytRU1X+S5pPOObaU9N8WS0jrcjZpvQJcDBzU5pDDypO0EDiUtMf6syWXMymSDgTOJ70PbwHuIq3PlwObks7LdnxEfKa0IvtI0j8AHwGWk/ZeP0S6svamwN3A3iN07kDrwNnsbK6SUc/mOuUyjFY2O5etV85l53KVOJedy1U2zNnsc3hXTEQcJelK4D2k8x9NI530/hvAP9VkT/U6wJwWj2891YUM0PqF26/KrZXLgcqGN6n+k4DXkq7KvDsgUoifC5wZEReUV56N0/XAl0gBtiWwMxCkEP8mcFpE/Ky88vorIo6RdBXwPtKyrgn8Fvg86T+DWp2nzEaQs7k2nM3O5ioamWx2LluvnMu14Vx2LlfRyOQyDHc2+z+8zczMzMzMzMzMzKwWfA5vMzMzMzMzMzMzM6sF/+BtZmZmZmZmZmZmZrXgH7zNzMzMzMzMzMzMrBb8g7eZmZmZmZmZmZmZ1YJ/8DYzMzMzMzMzMzOzWvAP3mZmZmZmZmZmZmZWC/7B28zMzMzMzMzMzMxqwT94W1eS5kuKQvurcfSfNTVV9l9xOcquZZhIWk3SsZJ+LunRwrr+YpfpFjZtR+NtCwvzWpwfWzDo5a0qSZtJ+ltJ/yvpIUkrJN0v6ZeSLszrcI6kaWXXambj41x2Lhc5l6vBuWxWX85l53KRc7kanMv1N73sAqySPinpOxHxTNmFWCnOBA4quwhrT9LbgK8BazeN2jC3lwFvyo/tClw7ddWZ2QA4l0ebc3nIOZfNRo5zebQ5l4ecc3k0+D+8bSJeAhxSdhE29SRtw1h4nw68GHhBbsd2mfzIQt/mdmXu89sOfY7s13LUmaQ9SV+y1gYeBBaQQnqT3OYARwNXlFSimfWfc3lEOZeHn3PZbCQ5l0eUc3n4OZdHh//D28brDtKH9t9IOjMiVpRdkE2pnQq3Px4RS3udMCKWActajZP0zFi3eKyHec3q9XlH0EnANGAp8KqIuLNp/H3AT4EvSNqeFPJmVl3O5dHmXB76oDh+AAAOwElEQVR+zmWz0eJcHm3O5eHnXB4R/g9vG68T83Ar4LAyC7FSrNm4MZ7wtqkhaXVgj3z3nBbhvZKIuCki7h98ZWY2QM7l0eZcHmLOZbOR5Fwebc7lIeZcHi3+wdvG63Lgx/n2xyWtNt4ZFC6qML9Dn73aXchD0qzCuL0kzZB0nKTrJT2WLzTwfUm7Nk23t6SLJN0r6SlJN0r6cK8XIZC0laSv5gtAPJXn821JO/Qw7XRJh0v6T0lLJC2X9ICkSyQdLEltplvpQiCStpD0JUm3SHoij1u3l/qb5vsmSedLukfSMkkPSlok6ShJq7bovzDXsLDwWPECGYvHW8NkdLoIR+FiH4vy/V0lnZ2X9UlJv5L0sRx2jWnWlXRC3iYezxetOC/v0e1Wy3qSPiHp6jzdMkl3SfqOpD/uMu3uks6UdEeu7QlJdypdOOOU5m24B+sz9rn+6DinbVXfGpI+KOnyvL0uz9vvBZLe2MP0kjQ3b2t359fmYUlXtNvW8nQrvf8lrZXXzw15/SzN2+u8yS6jWQ04l53LjcecyziXu0wvOZfNBs257FxuPOZcxrncZXrJuTw4EeHm1rEB84HIbRZpj1jj/lHd+rcY3xg3v8Nz7tVuHrmGxrgDgGsK94vtKWDfPM3xwLNt+n2rh+V+NfD7NtMvA97SYVleBFzXZtpG+wGwVpcadgMebjHtuuNYlzOAs7vUcj2wadN0C7tMs3iS29ii8cwHWJz7L2gxrlHrIuBQYEWbmv+DdFqnWcDNbfo8AuzUoY69gYe6vDYntpn2I12mC+D743wd1yps5z8Hpk1inexYeJ3btW+0ew5gPeCyLtNfA2zU5f2/G3BTh3l8YjLbnptbFRvOZeeyc7ldHc5l57Kb25Q3nMvOZedyuzqcy87l0lrpBbgNf6NFIAM/zPfvAlbv1r9pfGPc/A7PuVe7ebBygN+RP2Q/RDpsbCbwZuCePP52YF6+fSbpYgTrAy8HLijM50+6LPdvgHtJgbBpbocCSxgL8e1bzGMd4Lbc50HSxQ+2BdYFtgY+CjzRqK9LDXeRLlJxCLA5sDGwf/Pr32Vd/nNhfhcAu+fXbDvgM8DTedwvgNUK080gXdThyML0axfampPcxhbR/wC/O6+XHwGvy8u5DelqzI1lOJJ0fq57SIccbg5sBLw9b1cBXNWmhl1IXxID+CVwMLAlKbh2Ac4oPM8RTdNuU3itLwX+lPRFb2beNg8Avgl8ewKv5VWF5z0X2GUC83gRY19M7gTeCczOy7YD8OlC/X/XYvrphToeJ10IZMc8/SzgqML8LwdW6fD+vx14AHgPY+/xffNrHrmO7fr9uefmNswN57Jz2bncqgbnsnPZza2UhnPZuexcblWDc9m5XGorvQC34W+0DvA5hcc+0K1/0/h+BvgKYI8W07++qc+pLfqsSvoCEMB3uiz3Y8A2Lfpsy1gAX9Ri/D/mcY8AL22zrMVaX9WhhgeBzSexHncuzOvbgFr0OarQ5/2dXpM+b2OL6H+AB/B9WuxRJV3lurFt/AGY3aLPEYX5bNti/PV53HXAGm3qPCn3eaDYB3hffvw+Cl+U+vRa7snz99IvAS4ETgD2AWZ0mceFjH1p3LBNn79m7Mtr8384HF14fV/XZvqXAU/mfvOaxu1VqP3RNq//ZoX33in9fA3d3Ia94Vx2Lreop8/b2CKcy/16LZ3Lbm41bziXncst6unzNrYI53K/Xkvn8og0n8PbJiQirgYuznc/KmmNkkr5bkT8T4vHL2PsarrLgI81d4h0xezz8t05XZ7n1Ii4pcU8bgZOy3ffKGnjxjhJa5E+5CAdpvPrVjOOiEsZO8/bwR1q+IeIuKtLnZ00alkOfDDyp2BTLaeTgglSgFXdhyLimRaP/1seTgf+MSJub9Hnu6RwgHSI3nMk7U3aAwtpb/STbZ7/U6Q9thsAf1J4fHoePhARyzsvwvhExOXAG0j/KdGwMfAm4G9J7417JJ0s6QXN00t6Mek/ISBtJw+0eapvkPYmrwYc1DTu/Xn41Yj47zZ13gCcle922u6/nN9nzdPfTfpvBEj/iWI20pzLz83DuTzcnMuJc9ms5pzLz83DuTzcnMuJc7mG/IO3TcYJebgJaU9nGX7Y6sEcTnfkuz+JiEfaTN/44N6ky/Oc32Fc40vAKqTzJzXszthVmi+XtHa7Bvxf7veqDs9zcYdxvXhNHi7q8KEM8O95+LKJXOBjiNwREbe2GVcM7Hbb0KOkPc3w/O3j9Xn4EPDrDut1Gul8Z7Dyuv1FHu6QL7Yxs5cF6lVEXEY67G5/0mF5vyKdq6xhfdLhgVcXv3Rm+wLK/a/qsGxrMfZl77llk7Q16VA1gEVdtvtfNk/fwn90GNf4Utzt/Ws2KpzLiXN5ODmXnctmo8a5nDiXh5Nz2blca9O7dzFrLSJ+Lul7pHOAHSfpKxHx+BSXcU+HcY29iPf20KfbHvfn7TEr+FXh9paF2y8t3P5pl/k3bNhh3B0dxvWiUdtNXfrdmIcinZtq6SSftyy9bBswse2jsW5nkg6/68Vz6zYiFkm6ADgQOA74iKRrSYeO/Tdw2WTfSxHxNOlL38UAOTB3J52j71DSnubtSAH/5sKkjWVbhXRet14Ut9vidn/OBKZv1mk9PpGHa3boYzYynMvPcS4PJ+eyc9lspDiXn+NcHk7OZedyrfk/vG2yPkk6jGVD0nmWplqrw28m0qebx3ocVzzk5Y8m8DyrtxsREU+0G9ejRm2dlgXSOaCap6miXtd7L/3UdL8f6/atwDGkL2bTSIcJfhj4HnC/pC9LWmcCz9NSRDwWEZdExDtJ/72wLI86QNKLCl0nu2wTmX5Gh3ETWT9mo8y57FweVs7lAuey2chwLjuXh5VzucC5XD/+wdsmJSKuJ13ZFtJet3594A/b0Qdr9ziuGH4rBXtEqIc2q69Vr6xRW6dlaR7/aNteo62xbq/tcb0qIuYXZxARKyLisxExm3QF8kOAr5MumLEm8F7gMkl9fy9ExDX5uRp2brFsD45j2fZqMT3Ay3qdR7+X0WxUOZefN865PBqcy85ls6HkXH7eOOfyaHAuO5dL5x+8rR8WkM5fNBP4QA/9n8rDTodFbTrJmvpt2w7jtivcvrNwu3hI1Sv6W86ELM7D7bv02yEPA/jtwKqptsa63U5Sp72tPYmI2yLiXyPiHcAWpKuVQzpX1/7tp5yUGwu3i4c4NZZtA0mbT2C+xe1+57a9zGyQFuBcbnAujwbncnvOZbPyLcC53OBcHg3O5facy1PEP3jbpEXEjcDZ+e6H6X6IRuMcUC/t0OcNk62rz/68w7i35OGzwE8Kj1/O2GEwhw2iqHG6Mg/3lLRBh37z8vCGiKjq+cgG7ZI8XIt0qFXfRDqX2ILCQ9u16TpZxXAunvfrR4XbE9lub2DsPT4M273ZyHEuO5dHkHO5PeeyWcmcy87lEeRcbs+5PEX8g7f1ywLSuYPWpfu5ya7Ow3mSnnfyfEl70ucPxT54r6Rtmh+UtC1jV9z+QUTc1xgX6UrXZ+S78yXN7fQEktaR9MJ+FdxCo5YZwOfb1HAkY3vXvzbAWqruElJQAXyu1bZRJGlWcc+2pK0ldfr8nV24/VCvRUlaU9Kp3fY0S9oCeEe++yhj70ki4mbgB/nu8ZJ27zKvjSStV5g+gC/ku/tI+lCX6WdI2rJTHzObkAU4l53Lo8O5PDYv57LZcFqAc9m5PDqcy2Pzci6XxD94W19ExK+Bs/Ld2Z36At/Iw82AiyXNkbRe/lD7KOnDY/FgKp2wB4BFkg6RtImkF0o6BPgv0uEty0lXD272MeDXpPfaOZLOkLSnpI0LyzxX0teB3wF7DGoBIuI6xkL57ZLOlbSbpPUlbSvpFOC0PP464KuDqqXqckgdQroq9YbANZI+KWnn/HpuKGlHSYdLuhC4jZUvaPJx4HZJJ0vaT9IWktaVNFvSYcB5ud/jwEXjKG0V4D3AbyRdJOmIXMeGua4dJR0DXMvYlZ5PjIinmubzLuB+0mGU/yXpc3lb2UDSTEnbSfpLSd8hHZbY/J7/InBFvv15SedJekN+36wraStJ+0v6EukwwIPGsYxm1gPnsnN5lDiXnctmw8657FweJc5l5/JQiAg3t44NmE86P1UAszr0mw2sKPRt258UDtGmXQH8Wbt5ALMK4/bqUM+i3GdhL8vWZblfDSxtU+8yYG6H53gh6fCodstbbAf0Wt8E1+UM0uF0nWq4HthsvK/XJOtqrKvFPfZfnPsvaDFuYR63qMP0e/W4Tbd9njx+d+CuHtbr08B6LWrs1J4ADhzn67gG6SIYvWxrTwN/12Fe2wI39TCfZ4GdWky/DnBBj7W8b4LrZ8F4ths3t7o0nMvO5QHV02JdLe6x/2Kcy63qcS67uY1Aw7nsXB5QPS3W1eIe+y/GudyqHufyCLVhu7KvVVhE3C7pW8DhPXR/F/BT4J2kiz4EcCvwLeBU4DWDqnMiIuKnkl4JHA/sB2wCPAz8GPhUpPOytZv2XkmvBd4M/CUwB9iItHfxIeBm4IfAuRFx24CXYxnwVkkHkNbTHNLFUx4lHXJ0NvC1iFg+yDrqIiKuUjo863DgAGBHYH1SOC4B/g+4EPheRPy+MOlxwKXAvqRD4l5IWg9PkvZuXwqcGhHjughKRDwpaUPg9cDepIt4vCTPG+APpPfZFaQvtjd3mNfNknYkbbPzgFcCG5Deq/eTLuLxA+C8iLi7xfSPAAdK2oe0d/81pPfNaqQvw7cAl+Xprx/PcppZb5zLbad1LteUc9m5bDbMnMttp3Uu15Rz2blcJuVf/c3MzMzMzMzMzMzMKs3n8DYzMzMzMzMzMzOzWvAP3mZmZmZmZmZmZmZWC/7B28zMzMzMzMzMzMxqwT94m5mZmZmZmZmZmVkt+AdvMzMzMzMzMzMzM6sF/+BtZmZmZmZmZmZmZrXgH7zNzMzMzMzMzMzMrBb8g7eZmZmZmZmZmZmZ1YJ/8DYzMzMzMzMzMzOzWvAP3mZmZmZmZmZmZmZWC/7B28zMzMzMzMzMzMxq4f8BTNPcyW+6aC0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1584x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_df = pd.DataFrame(samples['observed_data'], columns = animals)\n",
    "\n",
    "plt.figure(figsize = (22, 8))\n",
    "for i, animal in enumerate(sample_df):\n",
    "    plt.subplot(1, 3, i+1)\n",
    "    sample_df[animal].value_counts().sort_index().plot.bar(color = 'r');\n",
    "    plt.xticks(range(7), range(7), rotation = 0);\n",
    "    plt.xlabel('Number of Times Seen'); plt.ylabel('Occurences');\n",
    "    plt.title(f'1000 Samples for {animal}');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interestingly, the most likely number of bears is zero! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dirichlet Distribution\n",
    "\n",
    "We can plot the Dirichlet Distribution as a triangle with colors indicating the value of the hyperpriors. This code is taken from the following sources.\n",
    "\n",
    "http://blog.bogatron.net/blog/2014/02/02/visualizing-dirichlet-distributions/\n",
    "\n",
    "https://gist.github.com/tboggs/8778945"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet(alphas))\n",
    "annotate_plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet(6 * pvals))\n",
    "annotate_plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Next Observation\n",
    "\n",
    "In order to find what we can expect from the next observation, we draw a single sample 10000 from a multinomial distribution. The probability of seeing each species is proportional to that obtained from the sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "next_obs = np.random.multinomial(n = 1, pvals = pvals, size = 10000)\n",
    "\n",
    "# Data manipulation\n",
    "next_obs = pd.melt(pd.DataFrame(next_obs, columns = ['Lions', 'Tigers', 'Bears'])).\\\n",
    "            groupby('variable')['value'].\\\n",
    "            value_counts(normalize=True).to_frame().\\\n",
    "             rename(columns = {'value': 'total'}).reset_index()\n",
    "next_obs = next_obs.loc[next_obs['value'] == 1]\n",
    "\n",
    "# Bar plot\n",
    "next_obs.set_index('variable')['total'].plot.bar(figsize = (8, 6));\n",
    "plt.title('Next Observation Likelihood');\n",
    "plt.ylabel('Likelihood'); plt.xlabel('');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>variable</th>\n",
       "      <th>value</th>\n",
       "      <th>total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bears</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Lions</td>\n",
       "      <td>1</td>\n",
       "      <td>0.4375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Tigers</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3317</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  variable  value   total\n",
       "1    Bears      1  0.2308\n",
       "3    Lions      1  0.4375\n",
       "5   Tigers      1  0.3317"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tuning vs Broken In Samples\n",
    "\n",
    "To see if the tuning samples display any major difference from those past the burn-in period, we can plot both distributions. Traditionally, the tuning samples are discarded."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_df = pd.melt(all_df, id_vars=['tune'], \n",
    "                   var_name='animal', value_name='posterior')\n",
    "\n",
    "plt.rcParams['font.size'] = 20\n",
    "g = sns.FacetGrid(data = all_df, hue = 'tune', col = 'animal', size = 6)\n",
    "g.map(sns.kdeplot, 'posterior');\n",
    "l = plt.legend(prop={'size': 20});\n",
    "l.set_title('Tune');\n",
    "g.set_ylabels(label = 'Density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.444018</td>\n",
       "      <td>0.152194</td>\n",
       "      <td>0.002562</td>\n",
       "      <td>0.152288</td>\n",
       "      <td>0.735601</td>\n",
       "      <td>2779.622971</td>\n",
       "      <td>1.000291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.330000</td>\n",
       "      <td>0.144525</td>\n",
       "      <td>0.002627</td>\n",
       "      <td>0.071472</td>\n",
       "      <td>0.610482</td>\n",
       "      <td>2727.795655</td>\n",
       "      <td>1.000087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.225982</td>\n",
       "      <td>0.130168</td>\n",
       "      <td>0.002613</td>\n",
       "      <td>0.014302</td>\n",
       "      <td>0.475272</td>\n",
       "      <td>2475.737395</td>\n",
       "      <td>0.999708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.444018  0.152194  0.002562  0.152288  0.735601  2779.622971   \n",
       "tigers  0.330000  0.144525  0.002627  0.071472  0.610482  2727.795655   \n",
       "bears   0.225982  0.130168  0.002613  0.014302  0.475272  2475.737395   \n",
       "\n",
       "            Rhat  \n",
       "lions   1.000291  \n",
       "tigers  1.000087  \n",
       "bears   0.999708  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Given the question posed, we can provide the following answers:\n",
    "\n",
    "__Estimated Prevalence__\n",
    "\n",
    "Below are the means and 95% HPD for the estimates\n",
    "\n",
    "* Lions: 44.5% (16.9% - 75.8%)\n",
    "* Tigers: 32.7% (6.7% - 60.5%)\n",
    "* Bears: 22.7% (1.7% - 50.0%)\n",
    "\n",
    "__Probability Next Observation is a Bear__\n",
    "\n",
    "Based on the sampling, 22.9%. \n",
    "\n",
    "(Results may change from one run to the next. This is due to the stochastic nature of MCMC). \n",
    "\n",
    "The best parts about Bayesian Inference are the incorporation of priors and the uncertainty inherent in the methods. With the scant evidence, we can provide estimates, but only with a large amount of uncertainty. More visits to the wildlife preserve would certainly help to clear up the matter! \n",
    "\n",
    "## Next Steps\n",
    "\n",
    "If we have more observations, we can simply add them to the model as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:07<00:00, 405.81draws/s]\n"
     ]
    }
   ],
   "source": [
    "c = np.array([[3, 2, 1],\n",
    "              [2, 3, 1],\n",
    "              [3, 2, 1],\n",
    "              [2, 3, 1]])\n",
    "\n",
    "with pm.Model() as model:\n",
    "    # Dirichlet hyperparameters are uniform hyperpriors\n",
    "    hyperpriors = pm.Uniform('hyperpriors', shape = 3, observed = alphas)\n",
    "    # Probabilities for each species\n",
    "    parameters = pm.Dirichlet('parameters', a=hyperpriors, shape=3)\n",
    "    # Observed data is a multinomial distribution with 6 trials\n",
    "    observed_data = pm.Multinomial(\n",
    "        'observed_data', n=6, p=parameters, shape=3, observed=c)    \n",
    "    \n",
    "    trace = pm.sample(draws=1000, chains=2, tune=500, discard_tuned_samples=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.403880</td>\n",
       "      <td>0.092552</td>\n",
       "      <td>0.001896</td>\n",
       "      <td>0.238665</td>\n",
       "      <td>0.597055</td>\n",
       "      <td>2172.218518</td>\n",
       "      <td>0.999828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.411601</td>\n",
       "      <td>0.090915</td>\n",
       "      <td>0.001975</td>\n",
       "      <td>0.243581</td>\n",
       "      <td>0.588124</td>\n",
       "      <td>2086.615145</td>\n",
       "      <td>0.999878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.184519</td>\n",
       "      <td>0.074620</td>\n",
       "      <td>0.001614</td>\n",
       "      <td>0.047123</td>\n",
       "      <td>0.325108</td>\n",
       "      <td>2052.651319</td>\n",
       "      <td>0.999501</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.403880  0.092552  0.001896  0.238665  0.597055  2172.218518   \n",
       "tigers  0.411601  0.090915  0.001975  0.243581  0.588124  2086.615145   \n",
       "bears   0.184519  0.074620  0.001614  0.047123  0.325108  2052.651319   \n",
       "\n",
       "            Rhat  \n",
       "lions   0.999828  \n",
       "tigers  0.999878  \n",
       "bears   0.999501  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = pm.summary(trace)\n",
    "summary.index = animals\n",
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainty of the prevalence of bears has descreased and the prevalence of the lions and tigers is nearly identical as expected. As we gather more data, we can incorporate it into the model to get more accurate estimates. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.plot_posterior(trace, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Altering Priors\n",
    "\n",
    "Below we change the alpha values which places more (higher values) or less (lower values) emphasis on the priors. With a greater emphasis, the posteriors are closer to each other, but with smaller emphasis, the posteriors are more reflective of the observations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# observations\n",
    "animals = ['lions', 'tigers', 'bears']\n",
    "c = np.array([3, 2, 1])\n",
    "alphas = np.array([10, 10, 10])\n",
    "\n",
    "def sample_with_priors(alphas):\n",
    "    with pm.Model() as model:\n",
    "        # Dirichlet hyperparameters are uniform hyperpriors\n",
    "        # hyperpriors = pm.Uniform('hyperpriors', shape = 3, observed = alphas)\n",
    "        # Probabilities for each species\n",
    "        parameters = pm.Dirichlet('parameters', a=alphas, shape=3)\n",
    "        # Observed data is a multinomial distribution with 6 trials\n",
    "        observed_data = pm.Multinomial(\n",
    "            'observed_data', n=6, p=parameters, shape=3, observed=c)    \n",
    "\n",
    "        trace = pm.sample(draws=1000, chains=2, tune=500, discard_tuned_samples=True)\n",
    "    return trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:03<00:00, 867.36draws/s] \n"
     ]
    }
   ],
   "source": [
    "t = sample_with_priors(np.array([10, 10, 10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.plot_posterior(t, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);\n",
    "    \n",
    "plt.suptitle(f'10 Prior', y = 1.05);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:04<00:00, 608.34draws/s]\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:05<00:00, 592.94draws/s] \n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 4 jobs)\n",
      "NUTS: [parameters]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:04<00:00, 613.20draws/s] \n"
     ]
    }
   ],
   "source": [
    "trace_dict = {}\n",
    "for alpha_array in [np.array([1, 1, 1]), np.array([0.1, 0.1, 0.1]), np.array([0.5, 0.5, 0.5])]:\n",
    "    trace_dict[str(alpha_array[0])] = sample_with_priors(alpha_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior = '0.1'\n",
    "trace = trace_dict[prior]\n",
    "\n",
    "ax = pm.plot_posterior(trace, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);\n",
    "    \n",
    "plt.suptitle(f'{prior} Prior', y = 1.05);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.486178</td>\n",
       "      <td>0.182540</td>\n",
       "      <td>0.004160</td>\n",
       "      <td>0.148061</td>\n",
       "      <td>0.827008</td>\n",
       "      <td>2239.025055</td>\n",
       "      <td>0.999525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.335813</td>\n",
       "      <td>0.173570</td>\n",
       "      <td>0.003993</td>\n",
       "      <td>0.041314</td>\n",
       "      <td>0.670795</td>\n",
       "      <td>1768.902027</td>\n",
       "      <td>1.000122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.178009</td>\n",
       "      <td>0.142854</td>\n",
       "      <td>0.003889</td>\n",
       "      <td>0.000356</td>\n",
       "      <td>0.457994</td>\n",
       "      <td>1697.039542</td>\n",
       "      <td>1.000073</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.486178  0.182540  0.004160  0.148061  0.827008  2239.025055   \n",
       "tigers  0.335813  0.173570  0.003993  0.041314  0.670795  1768.902027   \n",
       "bears   0.178009  0.142854  0.003889  0.000356  0.457994  1697.039542   \n",
       "\n",
       "            Rhat  \n",
       "lions   0.999525  \n",
       "tigers  1.000122  \n",
       "bears   1.000073  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = pm.summary(trace)\n",
    "summary.index = animals\n",
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a smaller weight on the priors, the data has a greater influence on the posterior. Therefore, the mean values are nearly equal to the prevalence in the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior = '0.5'\n",
    "trace = trace_dict[prior]\n",
    "\n",
    "ax = pm.plot_posterior(trace, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);\n",
    "    \n",
    "plt.suptitle(f'{prior} Prior', y = 1.05);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.466764</td>\n",
       "      <td>0.174351</td>\n",
       "      <td>0.003773</td>\n",
       "      <td>0.144898</td>\n",
       "      <td>0.787162</td>\n",
       "      <td>2071.791490</td>\n",
       "      <td>0.999827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.338432</td>\n",
       "      <td>0.164624</td>\n",
       "      <td>0.003766</td>\n",
       "      <td>0.061670</td>\n",
       "      <td>0.654715</td>\n",
       "      <td>1647.955237</td>\n",
       "      <td>1.000361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.194803</td>\n",
       "      <td>0.137118</td>\n",
       "      <td>0.003153</td>\n",
       "      <td>0.001019</td>\n",
       "      <td>0.465299</td>\n",
       "      <td>1844.063644</td>\n",
       "      <td>0.999649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.466764  0.174351  0.003773  0.144898  0.787162  2071.791490   \n",
       "tigers  0.338432  0.164624  0.003766  0.061670  0.654715  1647.955237   \n",
       "bears   0.194803  0.137118  0.003153  0.001019  0.465299  1844.063644   \n",
       "\n",
       "            Rhat  \n",
       "lions   0.999827  \n",
       "tigers  1.000361  \n",
       "bears   0.999649  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = pm.summary(trace)\n",
    "summary.index = animals\n",
    "summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior = '1'\n",
    "trace = trace_dict[prior]\n",
    "\n",
    "ax = pm.plot_posterior(trace, varnames = ['parameters'], \n",
    "                       figsize = (20, 10), edgecolor = 'k');\n",
    "\n",
    "plt.rcParams['font.size'] = 22\n",
    "for i, a in enumerate(animals):\n",
    "    ax[i].set_title(a);\n",
    "    \n",
    "plt.suptitle(f'{prior} Prior', y = 1.05);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lions</th>\n",
       "      <td>0.438157</td>\n",
       "      <td>0.160531</td>\n",
       "      <td>0.003407</td>\n",
       "      <td>0.127372</td>\n",
       "      <td>0.732571</td>\n",
       "      <td>2152.303466</td>\n",
       "      <td>0.999559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tigers</th>\n",
       "      <td>0.338736</td>\n",
       "      <td>0.149940</td>\n",
       "      <td>0.003392</td>\n",
       "      <td>0.069151</td>\n",
       "      <td>0.633109</td>\n",
       "      <td>1995.996050</td>\n",
       "      <td>0.999508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bears</th>\n",
       "      <td>0.223107</td>\n",
       "      <td>0.129539</td>\n",
       "      <td>0.002607</td>\n",
       "      <td>0.014103</td>\n",
       "      <td>0.474587</td>\n",
       "      <td>1904.705707</td>\n",
       "      <td>0.999663</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff  \\\n",
       "lions   0.438157  0.160531  0.003407  0.127372  0.732571  2152.303466   \n",
       "tigers  0.338736  0.149940  0.003392  0.069151  0.633109  1995.996050   \n",
       "bears   0.223107  0.129539  0.002607  0.014103  0.474587  1904.705707   \n",
       "\n",
       "            Rhat  \n",
       "lions   0.999559  \n",
       "tigers  0.999508  \n",
       "bears   0.999663  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = pm.summary(trace)\n",
    "summary.index = animals\n",
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the greatest emphasis on the priors, they play a larger role in the posterior estimates and therefore tend to bring the estimated posterior means closer together. The data has a smaller impact when the priors are greater.\n",
    "\n",
    "Overall, the choice of the hyperpriors depends on our confidence in the prior distribution. If we have good reason to believe all the animals are represented at the same frequency, then we should increase the weight of the priors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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